If x² + 1/x² = 102, then x -1/x =
a) 10
b) 8
c) 13
d) 12

Answer:

148.7804878

Step-by-step explanation:

All you have to do is divide!

Answer:

a=-2π

b=-17/3

c=-sqrt18

Step-by-step explanation:

eyeball it.

-2π≈-6.28

-17/3 is less than -5 but more than -6, so it's between those 2

-sqrt 18 is between -sqrt 16 and -sqrt 25, so it's a little less than -4

Answer:

1.4y

Step-by-step explanation:

[tex] \underline{\large \bf{Required \: Answer}} : - [/tex]

[tex] \dashrightarrow \: \red{\large8}[/tex]

[tex] \sf[/tex]

[tex] \underline{ \large{ \rm \pink{SolutioN}}} \: -[/tex]

[tex] \quad \qquad\sf \: {(a + b)}^{2} = 10[/tex]

[tex] \qquad \: \: \to\: \: \sf{a}^{2} + {b}^{2} + 2ab = 10[/tex]

[tex] \qquad\: \: \to\: \: \sf{a}^{2} + {b}^{2} + 2(1) = 10[/tex]

[tex] \qquad\: \: \to\: \: \sf \: {a}^{2} + {b}^{2} = 10 - 2[/tex]

[tex] \qquad\: \:\bf \to\: \: \: {a}^{2} + {b}^{2} = 8[/tex]

[tex] \sf[/tex]

[tex] \sf \therefore \: 8 \: \: is \: \: the \: \: required \: \: answer[/tex]

[tex] \rule{200pt}{2pt}[/tex]

Based on the triangle inequality theorem, the possible values of h in cm is: A. 4x < h < 10x

Based on the triangle inequality theorem, two sides of a triangle must be equal or more than the third sides.

Given a values of the side lengths of a triangle as, 3x, 6x, and h cm, the possible values would be determined as shown below:

h < 3x + 7x or 7x - 3x < h

h < 10x or 4x < h

The possible values of h would be: 4x < h < 10x.

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Answer:

7 yds  1 ft 1 inch

Step-by-step explanation:

Quick Solve!

Side #1:

144 inches + 24 inches + 7 inches = 175 inches

Side #2:

72 inches + 18 inches = 90 inches + 6 inches = 96 inches

Conclusion:

175 inches + 96 inches = 271 inches

Answer:

⇒ 7 yds  1 ft 1 inch

Answer:

7 yards 1 foot 1 inch

Step-by-step explanation:

Adding both of them together, you get:

6 yards 3 feet 13 inches

Since 1 foot = 12 inches, and 13 inches exceeds that, add a foot to the previous 3 feet and subtract 12 from the 13 inches

Therefore: 6 yards 4 feet 1 inch

Since 1 yard = 3 feet, and 4 feet exceeds that, add a yard to the previous 6 yards and subtract 3 feet from the remaining 4 feet

Hence:

7 yards 1 foot 1 inch

The probability that you lose all five times will be 0.59.

From the information given, the chances of winning are 0.1. Therefore, the chance of losing will be:

= 1 - 0.1 = 0.9

Therefore, the probability that you lose all five times will be:

= 0.9 × 0.9 × 0.9 × 0.9 × 0.9

= 0.59

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Answer:

January

Step-by-step explanation:

The month October is the 10th month,

there is 12 months in a year

2451 / 12 = 204.25

0.25 of a year, 1/4 of the year so 12/4 = 3

2451 months is 204 years and 3 months

3 months after October is January

10 + 3 = 13 where December is 12 and the 13th month is January

Answer:

4y^4

Step-by-step explanation:

This polynomial is supposed to be ordered:

-3x^4+4y^4+5x^2y^2-10xy^3+9x^3y

I dont totally understand the question but I hope the ordered polynomial helps

Answer:

10

Step-by-step explanation:

square root of 6^2 + 8^2

Answer:

6/- 3

Step-by-step explanation:

Answer:

Surface area of the composite figure = 508cm²

Step-by-step explanation:

Composite figures :- A composite shape is a 2D shape that is made from a combination of other basic 2D shapes and polygons. These shapes include squares, rectangles, triangles, circles.

Surface area of cuboid = 2(LB + LH + BH)

There are 2 cuboids in the question therefore solving them separately,

L = 12cm

B =  2cm

H = 10cm

putting these values in the above formula,

SA of bigger cuboid = 2(12×2 + 12×10 + 2×10)

                  SA           = 328cm²

L = 8cm

B =3cm

H = 6cm

SA = 2(8×3 + 8×6 + 3×6)

SA = 2×90

SA = 180cm²

now surface area of whole figure,

SA of bigger cuboid + SA of smaller cuboid

     328cm²   +    180cm²

       508cm² answer

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Answer:

B and D

Step-by-step explanation:

vertex(2,5) so D is correct

there are no real roots for the function B is correct

The circumference of the base of the cone is 8π - x since the base is equal to go the arc length of the remainder of the circle.

The radius r as a function of x will be:

8π - x = 2πr

r = (8π - x)/2π

r = 4 - x/2π

The height has a function of x will be:

r² + h² = 16

h² = 16 - r²

where r = 4 - x/2π

h = √16 - ✓(4 - x/2π)²

h = 4✓(4 - x/2π)²

The volume V of the cone as a function of x will be:

= 1/3 πr²h

= π/3(4 - x/2π)² 4✓(4 - x/2π)²

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Considering the direction of the wind, it is found that the jet travels faster than the sound during it's journey.

The jet's speed, considering that there is a tailwind, is given by:

J = Plane speed + Wind speed.

In this problem, we have that the speeds are given as follows:

Hence the jet's speed is given by:

J = 550 + 120 = 670 knots.

670 knots > 661 knots, hence the jet travels faster than the sound during it's journey.

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Answer:

r = 290°

Step-by-step explanation:

  In a triangle, exterior angles equals the sum of interior opposite angle.

In triangle A,

   x + 90 = 125   {Exterior angle property}

           x = 125 - 90

           x = 35°

In triangle B,

      y + 90 = 125

             y = 125 - 90

             y = 35°

    x + y + r = 360   {Complete angle}

35 + 35 + r = 360

         70 +r = 360

               r = 360 - 70

               r = 290°

Answer:

9 and 27

Step-by-step explanation:

let me know if you want an explanation

Answer:

C.

Step-by-step explanation:

IF YOU SEE A RIGHT ANGLED TRIANGLE APPLY THE TRIG RATIOS*

Answer:

the y intercept is (0,2)

slope = -4

Step-by-step explanation:

from the graph the y intercept is (0,2) and we can consider it as p1

p2 (2,-6)

slope = y2-y1 / x2-x1

= -6 - 2/ 2 -0 = -8/2 = -4

All the parts are answered , y =  6x + 5 represents the scatter data points given.

The complete question is

A coach is assessing the correlation between the number of hours spent practising and the average number of points scored in a game. The table shows the data:

Number of hours spent practising

(x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score in the game

(y) 5 8 11 14 17 20 23 26 29

Part A: Is there any correlation between the number of hours spent practising and the score in the game? Justify your answer. (4 points)

Part B: Write a function that best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate? (3 points)

A function is a law that connects the y and x variable , i.e. the dependent and independent variable.

Part (A)

There is a positive correlation between the number of hours spent practising and the score in the game , as the time is increasing the scores is also seen to be increasing.

Part (B)

From the online scatter point equation calculator or by using three points which best fits the linear regression the equation can be determined

y =  6x + 5

x represents the timeline spent in practising

Part C:

slope = 6

When the time spent practising increases by 1 hour,  the average scores increases by 1 hour, the score in a game is predicted to increase by an average of 6 and

as intercept = 5

When no time is spent on the practice the score obtained is 5.

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Using the outside angle theorem, the measure of angle CDE is: 70°.

According to the angle of intersecting tangents theorem, we would have the following equation using the diagram given:

Angle CDE = ½(measure of arc CBE - measure of arc CE)

Given the following:

Plug in the values into the equation

Angle CDE = ½(250 - 110)

Angle CDE = 70°

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Answer: Angle CDE = 70°

Step-by-step explanation:

Answer:

b(n) = -11 + (n-1)*8

Step-by-step explanation:

Let n be the sequence number, with n=1 the first number b(1) -11

The sequence changes by +8 each step.

b(1)   -11         + 8 =   -3

b(2)   -3          + 8 =    5

b(3)   5         + 8 =   13

b(4) 13

b(1) = -11

b(2) = -3.   or b(1) + 1*8

b(3) =  5,    or b(1) + 2*8

b(4) =  13,   or b(1) + 3*8

We note that each step adds a multiple of 8 to the initial value of -11.  This can be stated as (n-1)*8

The formula for this sequence would be b(n) = b(1) + (n-1)*8

b(n) = -11 + (n-1)*8

Check:  Does n=3 return the value of 5?

b(n) = -11 + (n-1)*8

b(3) = -11 + ((3)-1)*8

b(3) = -11 + (2)*8

b(3) = -11 + 16

b(3) = 5   YES

1. The range of the given function y = 3x² for the given domain: {- 2, - 1, and 0} is {12, 3, 0}.

2. The range of the given function y = 8x + 1, where x > 2 is (17, ∞).

3. The range of the given function y = 5x + 2, where x > -2 is (- 8, ∞).

We know that the range of a function is the entire set of all possible values for the dependent variable (typically y), after substituting the domain.

1. For the function y = 3x²,

Here the domain is {- 2, - 1, and 0}. So, we have to find the y values for the x values - 2, - 1, and 0 to find the range of the function.

Now, at x = - 2,

y = 3(- 2)² = 3 × 4 = 12

At x = - 1,

y = 3(- 1)² = 3 × 1 = 3

At x = 0,

y = 3(0)² = 3 × 0 = 0

So, the range of this function is {12, 3, 0}.

2. Now, for the function y = 8x + 1,

At x = 2,

y = 8 × 2 + 1 = 16 + 1 = 17

Since the domain is x > 2, we can say that the range set will contain values greater than 17.

So, the range of this function is (17, ∞).

3. For the function y = 5x + 2,

Now, at x = - 2,

y = 5 × (- 2) + 2 = - 10 + 2 = - 8

Since the domain is x > - 2, we can say that the range set will contain values greater than - 8.

So, the range of this function is (-8, ∞).

1. Therefore, the range of the given function y = 3x² for the given domain: {- 2, - 1, and 0} is {12, 3, 0}.

2. The range of the given function y = 8x + 1, where x > 2 is (17, ∞).

3. The range of the given function y = 5x + 2, where x > -2 is (- 8, ∞).

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Answer:

The answer would be D    7mn+3m/2+5n/4

Step-by-step explanation:

A polynomial is a combination of terms separated by +

or  − signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms.

Answer:

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

Step-by-step explanation:

Solving :

⇒ log y = log (x²)

⇒ log y = 2 log x

⇒ [tex]\mathsf {\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} \times 2}[/tex]

⇒ [tex]\mathsf {\frac{dy}{dx}= 2x}[/tex]

Answer:

y’ = 2x

Step-by-step explanation:

Let y = f (x), take the natural logarithm of both sides ln (y) = ln (f (x))

ln (y) = ln (x²)

Differentiate the expression using the chain rule, keeping in mind that y is a function of x.

Differentiate the left hand side ln (y) using the chain rule.

y’/y = 2 In (x)

Differentiate the right hand side.

Differentiate 2 ln (x)

y’/y = d/dx = [ 2 In (x) ]

Since 2 is constant with respect to xx, the derivative of 2 ln (x) with respect to x is 2 d/dx [ln (x)]

y’/y = 2 d/dx [In (x)]

The derivative of ln (x) with respect to x is 1/x.

y’/y = 2 1/x

Combine 2 and 1/x

y’/y = 2/x

Isolate y' and substitute the original function for y in the right hand side.

y’ = [tex]\frac{2}{x}[/tex] x²

Factor x out of x².

y’ = [tex]\frac{2}{x}[/tex] (x * x)

Cancel the common factor.

y’ = [tex]\frac{2}{x}[/tex] (x * x)                     (The x that is under 2 and the other x that I have underlined are the ones that cancel out)  

Rewrite the expression.

y’ = 2x

So therefore, the answer would be 2x.

Answer:

1.596

Step-by-step explanation:

So you can rewrite log as: [tex]log_{b}a=x = > b^x=a[/tex] So in this case it's already in exponential form which we'll use to rewrite into logarithm form.

[tex]4^{x+3} = 7\\log_47=x+3\\\\\frac{log7}{log4}=x+3\\1.404\approx x+3\\x\approx1.596[/tex]

Answer:

x = -1.596

Explanation:

[tex]\rightarrow \sf 4^{x + 3} = 7[/tex]

take log on both sides

[tex]\rightarrow \sf log(4^{x + 3}) = log(7)[/tex]

[tex]\rightarrow \sf (x + 3)log(4) = log(7)[/tex]

[tex]\rightarrow \sf x + 3= \dfrac{log(7)}{log(4)}[/tex]

[tex]\rightarrow \sf x= \dfrac{log(7)}{log(4)} -3[/tex]

calculate

[tex]\rightarrow \sf x= -1.596322539[/tex]

[tex]\rightarrow \sf x= -1.596 \quad (rounded \ to \ nearest \ thousand)[/tex]

Polynomial is an expression that consists of indeterminates(variable) and coefficients. The roots of the polynomial are ​1, 2.7321, and -0.7321.

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

The roots of the polynomial are:

x³ - 3x² + 2

If we divide the polynomial by (x-1), then

(x³ - 3x² + 2)/(x-1) = x² - 2x - 2

now, factorize the given polynomial,

x² - 2x - 2

x = 1 ± √3

x = ​1, 2.7321, -0.7321

​Hence, the roots of the polynomial are ​1, 2.7321, and -0.7321.

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The volume of the air space surrounding the cone inside the cylinder is 1055.04 cm³

The volume of the air space surrounding the cone inside the cylinder is as follows:

volume of the air space = volume of cylinder - volume of a cone

volume of cylinder = πr²h

volume of cylinder = π16 × 5²

volume of cylinder = 400π

volume of the cone = 1 / 3 πr²h

volume of the cone = 1 / 3 × π × 12 × 4²

volume of the cone = 64π

Therefore,

volume of the air space = 400π - 64π

volume of the air space = 336π

volume of the air space = 1055.04 cm³

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Answer:

3.75

Step-by-step explanation:

if 2.25 is the cost for 9 hrs then divide by 9 and find one hr. (.25$) then multiply by 15 hrs and kabam you have it