The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.

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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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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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:

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:

1.4y

Step-by-step explanation:

5b+a-2c when a=2,b=1&c=3

5(1) + 2 - 2(3)

5 + 2 - 6

7-6

Answer: 1

Answer:

s = 6 cm

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length )

given A = 36 , then

s² = 36 ( take square root of both sides )

s = [tex]\sqrt{36}[/tex] = 6

Answer:

148.7804878

Step-by-step explanation:

All you have to do is divide!

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]

Answer:

See below

Step-by-step explanation:

If you can't tell just by looking at them, you will need to convert them all to fractions of a common denominator .....in this case (the smallest) common denominator would be 18

1/2 = 9/18  

1/3 = 6/18

1/6 = 3/18

4/9 = 8/ 18             so now you can see least to greatest is

                                    1/6    1/3    1/2   4/9

Answer:

The linear measure of arc vw as described in the task content is; 46.89in.

It follows from the task content that the radius of the circle with center p is given as pv = 32in. and the angle subtended by the arc is; 84.

On this note, the measure of arc vw is;

= (84/360) × 2 × 3.14 × 32

= 46.89 inches.

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Answer:

9 and 27

Step-by-step explanation:

let me know if you want an explanation

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:

10

Step-by-step explanation:

square root of 6^2 + 8^2

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: 63

Step-by-step explanation:

I assume you meant (x+3)/5 = 12.

Answer:

C.

Step-by-step explanation:

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

Answer:

x = 45 degrees

Step-by-step explanation:

Using the alternate exterior angle theorem, the angles are equal. You can set the expressions equal to each other:

3x = x + 90
2x = 90
x = 45

Answer: The answer is

x=   -3

y=    3

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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The true statements about ∠MJK and ∠MJL are

The statement is given as:

∠MJK and ∠MJL are a linear pair of angles and the angles are also supplementary

As a general rule, linear pair angles are adjacent angles that add up to 180 degrees. This means that:

The above means that, the following options are true:

(e), (f) and (h)

Also, the converse of the statement is:

∠MJK and ∠MJL are supplementary angles and the angles are also  linear pair of angles

This is false because not all supplementary angles are  linear pair angles

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Answer:

Roots of the equation are  (−3−√7) , (−3+√7)

Step-by-step explanation:

For solving a quadratic equation using completing the square method:

given equation:

y = x^2 - 6x +2

0 = x^2 - 6x + 2

0 = x^2 - 3^2 + 3^2 -6x +2

0 = (x-3)^2 -7

7 =  (x-3)^2

±[tex]\sqrt{7}[/tex] = x-3

±[tex]\sqrt{7}[/tex] + 3 = x

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Answer:

By splitting the line segments into equal parts, we find that the length of the line segment formed by joining the mid-points is 5.5 units.

Step-by-step explanation:

Given lengths show that the length of JK is 5 units, KL is 4 units and LM is 6 units. Let the midpoint of JK be A. This means JK is splited into two equal parts JA and AK. Since the lengths of both the segments are same, it will be 5/2 = 2.5 units.

Now, let the midpoint of LM be B. So, we have two equal line segments LB and BM of length 6/2 = 3 units.

So, the length of the line segment formed by joining A and B will be 2.5 + 3 = 5.5 units

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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

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:

6/- 3

Step-by-step explanation:

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.

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: