5) The solution of (2x - 1)2 = 9 is equal to
d) 21
a) - 1
b) 2
c) - 1,2
d) None of these
6) The GCD of x2 - 2xy + y2​

Answer: Step 1

Find the scale factor

we know that

If the two cylinders are similar

then

The ratio between the circumference of the larger cylinder to the circumference of the smaller cylinder is equal to the scale factor

Step 2

Find the lateral area of the smaller cylinder

we know that

If the two cylinders are similar

then

The ratio between the lateral area of the larger cylinder to the lateral area of the smaller cylinder is equal to the scale factor squared

Let

x--------> the lateral area of the larger cylinder

y-------> the lateral area of the smaller cylinder

z--------> the scale factor

In this problem we have

substitute in the formula and solve for y

therefore

the answer is

33.6π mm2

The correct option is Option D: the lateral area of the smaller cylinder is 84π mm².

The lateral area of the cylinder is the area of the curved surface which can be calculated by the formula given below

lateral area of the cylinder= 2πrl

where r is the radius of the cylinder and l is the length of the cylinder.

Here given that the two cylinders are similar.

The larger cylinder has base of circumference = 60π mm

As we know the circumference of base of cylinder= 2πR

⇒60π= 2πr

⇒2πR= 60π

Given the lateral area of the larger cylinder is 210π mm²

From above formula, it is clear that the lateral area of the cylinder= 2πrl

⇒ 210π = 2πrl

⇒2πRl= 210π

⇒60πl= 210π (as from above it is derived that 2πr= 60π)

⇒l= 210π/ 60π= 7/2

⇒l= 3.5 mm

the smaller cylinder has base of circumference = 24π mm

⇒ 2πr= 24π mm

then the lateral area of the smaller cylinder is= 2πrl= 24π*3.5= 84π mm²

Therefore the correct option is Option D: the lateral area of the smaller cylinder is 84π mm².

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we know by looking at the picture that m is the midpoint of AB since O to M doted lines had half into two equal parts.so M is in the midpoints of AB.

Step-by-step explanation:

    to prove:  M is the midpoint of AB

         given:  OM is perpendicular to AB

construction: joint AO and BO

           proof: in the given fig,

                      OA and OB are joined

                      In Δ AOM and ΔBOM

                     AO = BO ( two sides of Δ AOB )

                    OM = OM ( common )

                   ∴ Δ AOM ≅ Δ BOM ( by SAS rule )

                    ∴ AM = BM ( by CPCT ) -------- 1

                    ∴ M is the midpoint of AB ( from 1 )

                                 ⇒hence proved

 HOPE THIS HELPED and PLEASE MAKE ME AS THE BRAINLIEST

Answer:

m<x = 60

Step-by-step explanation:

This triangle seems to be a 30-60-90 triangle, therefore m<x will be 60 degrees.

Answer:

n = 132

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

n is an exterior angle of the triangle, thus

n = 90 + 42 = 132

Answer:

n = 132

Step-by-step explanation:

Answer:

Las mujeres representan el 50.63% de la población.

Step-by-step explanation:

Este problema es un problema de proporciones el cual puede resolverse usando una regla de tres.

El problema nos dice que la población total de Colombia es de 49,821,512 y nos pide calcular qué porcentaje representa el total de mujeres que es igual a 25,228,444. Si llamamos x al porcentaje de mujeres podemos representar esto de la siguiente manera mediante una regla de tres:

Población      Porcentaje

49, 821,512       100%

25,228,444        x%

Resolviendo para x tenemos que:

[tex]x=\frac{25,228,444(100)}{49,821,512}=\frac{2,522,844,400}{49,821,512}= 50.6376[/tex]

Por lo tanto, las mujeres representan el 50.63% de la población.

Answer:

If you wish to find any term (also known as the {n^{th}}n  

th

 term) in the arithmetic sequence, the arithmetic sequence formula should help you to do so. The critical step is to be able to identify or extract known values from the problem that will eventually be substituted into the formula itself.

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

A transformation of a point is the movement of an point from an initial position to a new position. If an object is transformed, all the point of an object is transformed. Two figures are said to be congruent if they have the same shape and the measure of each of their sides are the same.

An object is congruent to another object if the object can be mapped to the other object when transformed.

Answer:

The answer is c

Step-by-step explanation:

It is the correct solution because you are able to map circle m onto m

Answer: C. Yes, this means more rainfall causes apple trees to produce more fruit.

Step-by-step explanation:

A positive correlation exists when one variable increases as the other variable increases.

Therefore, a strong positive linear correlation between rainfall and the number of apples a tree produces definitely means that increase in rainfall will increase the a production of apple fruit.Therefore, a strong positive linear correlation between rainfall and the number of apples a tree produces means that more rainfall causes apple trees to produce more fruit.

Yes, this means more rainfall causes apple trees to produce more fruit.

We have given that,

There is a strong positive linear correlation between rainfall and the number of apples a tree produces.

A positive correlation exists when one variable increases as the other variable increases.

Therefore, a strong positive linear correlation between rainfall and the number of apples a tree produces definitely means that increase in rainfall will increase the production of apple fruit. Therefore, a strong positive linear correlation between rainfall and the number of apples a tree produces means that more rainfall causes apple trees to produce more fruit.

Option C is correct.

Yes, this means more rainfall causes apple trees to produce more fruit.

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Answer:

B

Step-by-step explanation:

There is a difference of 2 between consecutive odd integers.

let n , n + 2 and n + 4 be the 3 consecutive odd integers, then

n + n + 2 + n + 4 = 87 , that is

3n + 6 = 87 ( subtract 6 from both sides )

3n = 81 ( divide both sides by 3 )

n = 27, n + 2 = 27 + 2 = 29, n + 4 = 27 + 4 = 31

Thus

The 3 consecutive odd integers are 27, 29, 31 → B

Answer:

a. TRUE.

Step-by-step explanation:

If the pair of opposite sides are both parallel and congruent, the other two sides will have to fit in between the two lines. That will make the other two sides both parallel and congruent, so the quadrilateral is a parallelogram.

Answer:

a. True

Step-by-step explanation:

A parallelogram is a quadrilateral. A parallelogram has two pairs of opposite parallel sides. The opposite parallel sides are equal in length and are congruent.

Answer:

One

Step-by-step explanation:

It is given that,

y = 3x-5 ....(1)

y = -x+4 .....(2)

We can solve the above equations using substitution method. Put the value of y from equation (1) to equation (2) such that,

[tex]3x-5 = -x+4\\\\3x+x = 5+4\\\\4x = 9\\\\x=\dfrac{9}{4}[/tex]

Put the value of x in equation (1) we get :

[tex]y = 3x-5\\\\y = 3\times \dfrac{9}{4}-5\\\\y=\dfrac{7}{4}[/tex]

It means that the value of x is [tex]\dfrac{9}{4}[/tex] and the value of y is [tex]\dfrac{7}{4}[/tex]. Hence, the given equations has only one solution.

Answer:

1

Step-by-step explanation:

Answer:

D. 35°

Step-by-step explanation:

1. The bottom right angle and 95° add up to 180°. Solve for that angle.

95 + y = 180

y = 85

2. Triangles have a total of 180°. Set up the equation.

60 + 85 + x = 180°

3. Simplify

145 + x = 180

4. Solve for x by subtracting 145 from both sides

x = 35°

Answer:

x = 35

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

60+x = 95

Subtract 60 from each side

60 +x-60 = 95-60

x = 35

Answer:

9! means 9 factorial

Step-by-step explanation:

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Answer:

[tex]-16x^{2} y^{2}z^{2}[/tex]

Step-by-step explanation:

Let's calculate the answer to the second parenthesis. Just multiply throughout to get -8xyz. Then, multiply the first parenthesis by the second. Multiply the constants (-8 and 2) first to get -16, multiply the x's together to get x^2, the y's together to get y^2, and the z's together to get z^2. Put it all together to get [tex]-16x^{2} y^{2}z^{2}[/tex].

Answer:

Your correct answer is = −16y2z2

Answer:

v = 50b / v = 50 × b

Step-by-step explanation:

1 bottle of subercharge = 50 vitamins

v = the total number of vitamins

b = number of bottles

For getting the answer of the total number of vitamins (v) you need to multiply the whole number of bottles (b) with the amount of vitamins present in a one bottle (50 vitamins). So , the answer is v = 50 × b / v =50b..Don't get confused both are the same.

Hope this helps and pls mark as brainliest : )

Answer: V=50b

Step-by-step explanation:

I got it right.

Answer:

720 ways

Step-by-step explanation:

At first their are six books, that means that there are six different positions to put them. The first book to be placed would have 6 position, when the first book is placed, to place the second book there would be 5 position since one position has been used by the first book. After placing the second book, to place the third book there would 4 available position, and it follows this manner i.e for the fourth book 3 available position, for the fifth book 2 available position and for the sixth book, one available position.

Therefore the number of ways to arrange the books on the shelf from left to right = 6 × 5 × 4 × 3 × 2 × 1 = 6! = 720 ways

Answer:

3. 7/12.

4. 7/5.

5. 1.

Step-by-step explanation:

The slope of a line can be obtained by taking the ratio of change in y-coordinate to that of x-coordinate. Mathematically, it is expressed as:

Slope = Δy /Δx

Δy = y2 – y1

Δx = x2 – x1

With the above formula in mind, let us answer the questions given above.

3. Point => (–8, –2) (4, 5)

x1 = –8

x2 = 4

Δx = x2 – x1

Δx = 4 – –8

Δx = 4 + 8

Δx = 12

y1 = –2

y2 = 5

Δy = y2 – y1

Δy = 5 – – 2

Δy = 5 + 2

Δy = 7

Slope = Δy /Δx

Slope = 7/12

4. Point => (3, –5) (8, 2)

x1 = 3

x2 = 8

Δx = 8 – 3

Δx = 5

y1 = –5

y2 = 2

Δy = y2 – y1

Δy = 2 – – 5

Δy = 2 + 5

Δy = 7

Slope = Δy /Δx

Slope = 7/5

5. Point => (–4, –5) (4, 3)

x1 = –4

x2 = 4

Δx = x2 – x1

Δx = 4 – –4

Δx = 4 + 4

Δx = 8

y1 = –5

y2 = 3

Δy = y2 – y1

Δy = 3 – – 5

Δy = 3 + 5

Δy = 8

Slope = Δy /Δx

Slope = 8/8

Slope = 1

Answer:

1. 3

2. 12

3. 27

Step-by-step explanation:

Answer:

1. 3                2. 12                3. 27

Step-by-step explanation:

1. 25's perfect square would be 5. 81's would be 9. 100's is 10. 121's is 11. So therefore, that would leave you with 3.

2. 4's is 2. 9's is 3. 144 is 12. 36 is 6. Therefore, 12 is not a perfect square.

3. The perfect square of 1 is obviously 1. 16 is 4, 49 is 7, and 64 is 8. So, 27 is the odd one out.

I really hope this helped! Good luck :)

Answer:

=-0.809

Step-by-step explanation:

3x^2+5x+7=0 complete the square

3x^2+5x=-7 divide both sides by 3

x^2+5/3 x = -7/3  to complete the square add term(b/2)^2=((5/3)/2)²=25/36

X^+5/3 x+25/36=-7/3 +25/36 factorize

(x+5/6)²= -59/36

x+5/6= + or - √59/36

solution for x= -5/6-√59/6i  (u) OR -5/6+√59/6i (v)

u/v + v/u=(-5/6-√59/6i)/(-5/6+√59/6i) +(-5/6+√59/6i)/(-5/6-√59/6i)=-17/21

=-0.809

Answer:

[tex]\large \boxed{\sf \ \ \ -\dfrac{17}{21}=-0.80952... \ \ \ }[/tex]

Step-by-step explanation:

Hello,

First of all we can verify that 0 is not a solution of the equation so that we can divide by u or v

[tex]\dfrac{v}{u}+\dfrac{u}{v}=\dfrac{u^2+v^2}{uv}=\dfrac{(u+v)^2-2uv}{uv}=\dfrac{(u+v)^2}{uv}-2[/tex]

And we know that

[tex]u+v=-\dfrac{5}{3}\\\\uv=\dfrac{7}{3}\\\\\\as \ \ (x-u)(x-v)=x^2-(u+v)x+uv[/tex]

So it comes

[tex]\dfrac{v}{u}+\dfrac{u}{v}=\dfrac{5^2*3}{7*3^2}-2=\dfrac{25-42}{21}=-\dfrac{17}{21}=-0.80952...[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: 6m^2 +m -40

Step-by-step explanation: Distributing binomials calls for the FOIL method.

Multiply the First times the First: 3m×2m= 6m^2. (^2 means squared when we can't use superscript for exponents.)

Then multiply and combine the Outside and Inside terms: 2m ×8=16m. and -5 ×3m= -15m

16m - 15m = m

Then multiply the Last terms: -5×8= -40

You end up with

6m^2 + m -40

Answer:

6m^2 + m - 40.

Step-by-step explanation:

(2m - 5)(3m + 8)

= (2m * 3m) + (-5 * 3m) + (2m * 8) + (-5 * 8)

= 6m^2 - 15m + 16m - 40

= 6m^2 + m - 40.

Hope this helps!

Answer:

B. 259.8 u²

Step-by-step Explanation:

The area of a regular hexagon is given as:

[tex] Area = \frac{3\sqrt{3} }{2} a^{2} [/tex]

Where a = side length of the hexagon

Thus, the area of the regular hexagon with a given side length, a = 10, is calculated as follows:

[tex] Area = \frac{3\sqrt{3} }{2} a^{2} [/tex]

[tex] Area = \frac{3\sqrt{3} }{2}* 10^{2} [/tex]

[tex] = \frac{3\sqrt{3} }{2}* 100 [/tex]

[tex] = \frac{3*1.7321 }{2}* 100 [/tex]

[tex] = \frac{5.1963 }{2}* 100 [/tex]

[tex] = \frac{519.63 }{2} [/tex]

[tex] Area = 259.815 [/tex]

The area of the regular hexagon ≈ 259.8 u²

Answer:

The correct option is;

(2·x - y = -2 and 22·x + 10·y = 7)

2 x minus y = negative 2 and 22 x + 10 y = 7

Step-by-step explanation:

2x - y = -2.........(1)

3x + 2y = 5.......(2)

4x - y = 2..........(3)

22x + 10y = 7...(4)

Given that the solution of the system of equation is (-0.3, 1.4), we have;

The system of equations consist of those equations that pass through the point (-0.3, 1.4)

We check as follows;

Equation (1)

2×(-0.3) - 1.4 = -2

Therefore, equation (1) passes through the point (-0.3, 1.4) and is one of the equations

Equation (2)

3×(-0.3) + 2×1.4 = 1.9 ≠ 5

Equation (2) is not part of the system of equations

Equation (3)

4×(-0.3) - 1.4 = -2.6 ≠2

Equation (3) is not part of the system of equations

Equation (4)

22×(-0.3) + 10×1.4 = 7.4 ≈ 7

Therefore, equation (4) approximately passes through the point (-0.3, 1.4) and is one of the equations

The correct option is A. [tex]2x - y = -2\ and 22x + 10y = 7.[/tex]

Given equations,

[tex]2x - y = -2.........(1)[/tex]

[tex]3x + 2y = 5.......(2)[/tex]

[tex]4x - y = 2..........(3)[/tex]

[tex]22x + 10y = 7...(4)[/tex]

Since the solution of the system of equation is [tex](-0.3, 1.4),[/tex]  Hence the system of equation satisfy the above point.

Now check all the equations,

Equation (1),

[tex]2\times(-0.3) - 1.4 = -2\\-0.6-1.4=-2\\-2.0=-2[/tex]

Hence, equation (1) passes through the point[tex](-0.3, 1.4)[/tex]  and is one of the equations.

Similarly, Equation (2)

[tex]3\times (-0.3) + 2\times1.4 = 5\\-0.9+2.8=5\\1.9=5\\[/tex]

Hence the above equation does not satisfy the solution, so it is not the other system of equation.

Now, Equation (3)

[tex]4\times(-0.3) - 1.4 = -2.6 \neq 2[/tex]

Hence Equation (3) is not part of the system of equations.

Now, Equation (4)

[tex]22\times (-0.3) + 10\times1.4 = 7.4[/tex]

Hence the above equation approximately passes through the solution[tex].(-0.3, 1.4)[/tex] and is one of the equations.

Hence the required system of equation is  [tex]2x - y = -2[/tex] and [tex]22x + 10y = 7[/tex].

Therefore the correct option is A.

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Answer:

94

Step-by-step explanation:

Add the three distances.

23 + 42 + 29 = 94

94 miles

[tex]\text{We need to get the total miles Milicent cycled}\\\\\text{To do this, we would add up all the distances she travelled}\\\\\text{Add:}\\\\23+42+29=94\\\\\boxed{\text{94 miles}}[/tex]

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

Explanation:

Any triangle prism is composed of 2 parallel triangular faces (base faces), along with 3 rectangular lateral faces.

The bottom triangle face has a base of 10 cm and a height of 4 cm. The area is 0.5*base*height = 0.5*10*4 = 20 square cm. Two of these triangles combine to an area of 2*20 = 40 square cm. We'll use this later.

The lateral surface area of any prism can be found by multiplying the perimeter of the base by the height of the prism. The base triangle has side lengths 5, 8 and 10. The perimeter is 5+8+10 = 23. So the lateral surface area is (perimeter)*(height) = 23*9 = 207

Add this to the total base area we got earlier and the answer is 40+207 = 247. The units are in square cm, which we can write as cm^2.

Answer:

855.298 m^3

Step-by-step explanation:

The volume of a cylinder equation is piR^2H.

So pi5.5^2×9

855.298 m^3

Answer:

The correct options are;

g(x) = -0.27·x² + x  + 5

h(x) = 2·㏒(x + 1) + 5

Step-by-step explanation:

To answer the question, we substitute x = 1.9 seconds into the given options as follows;

1) For f(x) = √(1.6·x) + 5

When x = 1.9 seconds, we have;

y = f(1.9) = √(1.6×1.9) + 5 = 6.74 which is not equal to the given height of 5.9 meters

Therefore, f(x) = √(1.6·x) + 5 does not model the height of the drone y as a function of time, x

2) For g(x) = -0.27·x² + x  + 5

When x = 1.9 seconds, we have;

y = g(1.9) = -0.27×1.9^2 + 1.9  + 5 = 5.93 meters, which is approximately 5.9 meters to one place of decimal

Therefore, the function, g(x) = -0.27·x² + x  + 5,  approximately models the height of the drone y as a function of time, x

3) For h(x) = 2·㏒(x + 1) + 5

When x = 1.9 seconds, we have;

y = h(1.9) = 2·log(1.9 + 1) + 5 = 5.92 meters,

The function, h(x) = 2·㏒(x + 1) + 5,  approximately models the height of the drone y as a function of time, x

4) For j(x) = -∛(-1.4·x - 1) + 5

When x = 1.9 seconds, we have;

y = j(1.9) = -∛(-1.4×1.9 - 1) + 5 = 6.54 meters

The function j(x) = -∛(-1.4·x - 1) + 5 does not model the height of the drone y as a function of time, x

5) For k(x) = -1.2·x³ + 2.6·x² - 0.5·x + 5

When x = 1.9 seconds, we have;

y = k(1.9) = -1.2×1.9^3 + 2.6×1.9^2 - 0.5×1.9 + 5 = 5.21 meters

Therefore, the function, k(x) = -1.2·x³ + 2.6·x² - 0.5·x + 5, does not model the height of the drone y as a function of time, x

Incomplete question. However, let's assume this are feasible regions to consider:

Points:

- (0, 100)

- (0, 125)

- (0, 325)

- (1, 200)

Answer:

Maximum value occurs at 325 at the point (0, 325)

Step-by-step explanation:

Remember, we substitute the points value for x, y in the objective function P = 2x + 1.5y.

- For point (0, 100): P= 2(0) + 1.5 (100) =150

- For point (0, 125): P= 2(0) + 1.5 (125) =187.5

For point (0, 325): P= 2(0) + 1.5 (325) = 487.5

For point (1, 200): P= 2(1) + 1.5 (200) = 302

Therefore, we could notice from the above solutions that at point (0,325) we attain the maximum value of P.

Answer:

Step 1: 4

Step 2: 4 and 1

Step 3: 2x² + 4x + x + 2

Step 4: (2x² + 4x) + (x + 2)

Step 5: 2x(x + 2) + 1(x + 2)

Step 6: (x + 2)(2x + 1)

Step-by-step explanation:

Answer: 82%

Step-by-step explanation:

- - - - - - - - college - - not college - - - - total

Travel - - - - 43 - - - - - - - 10 - - - - - - - - 53

Not travel - 24 - - - - - - - 5 - - - - - - - - - 29

Total - - - - 67 - - - - - - - 15 - - - - - - - - - 82

Marginal relative frequency of students who plan to attend college:

(Number of students who plan to attend the college / Total number of the students)

Number of students who plan to attend college = 67

total number of students = 82

Marginal relative frequency = 67/82

= 0.8170731

= (0.8170731) * 100%

= 81.7% = 82%

Answer:

a: 14/50

b: 15/50

c: 21/50

Step-by-step explanation:

on edge

Answer:

x = 8

or

x = -4

Step-by-step explanation:

3x² - 12x = 96

Divide both sides by 3

x² - 4x = 32

Add 4 to both sides

x² - 4x + 4 = 32 + 4

(x - 2)² = 6²

Find the square root of both sides

√(x - 2)² = √6²

x - 2 = +/- 6

x - 2 = +6 or -6

x - 2=+6

x=6+2

x=8

x - 2=-6

x=-6+2

x=-4

x = 8

or

x = -4