The sum of three consecutive numbers is 36. What are the numbers?

Answer:

x=11 I hope it helps you

Step-by-step explanation:

Answer:

it has to be whole numbers

Step-by-step explanation:

because all of them are whole number no matter if there negative or positive

The Horizontal stretch of the function f(x)=3x-9 by a factor of 6 is g(x)=x/2-9 .

The graph of the function y=f(x/a) represents a Horizontal Stretch by a factor of a of the graph y=f(x)    , where a>0 and a≠1 .

To find the horizontal stretch we divide the input by a ,

In the given question

f(x)=3x-9 , is horizontally stretch by a factor of 6.

So we divide the inputs by 6 .

On dividing the inputs by 6 , we get

f(x/6)=3(x*1/6)-9        (...as 3/6=1/2)

Let g(x) represents the horizontal stretch of f(x) by factor 6 , So

g(x)=x/2-9

Therefore , the Horizontal stretch of the function f(x)=3x-9 by a factor of 6 is g(x)=x/2-9 .

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Answer:

(-4,-3)

Step-by-step explanation:

Answer:

0.492 is the answer

Step-by-step explanation:

The probability that the two students are the same sex is 0.49.

Since the class contain 32 (18+14) children out of which  18 girls and 14 boys.

First step

Using general multiplication rule

P(Two girls)=P(First girls)×P(Second girl; First girl)

P(Two girls)=18/32×17/31

P(Two girls)=18×17/32×31

P(Two girls)=306/992

P(Two boys)=P(First boys)×P(Second boys; First boys)

P(Two girls)=14/32×13/31

P(Two girls)=14×13/32×31

P(Two girls)=182/992

Second step

Use addition rule for mutually exclusive events

P(Same sex)=P(Two girls)×P(Two boys)

P(Same sex)=306/992×182/992

P(Same sex)=306+182/992

P(Same sex)=488/992

P(Same sex)=61/124

P(Same sex)=0.49

Inconclusion the probability that the two students are the same sex is 0.49.

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Answer:

D

Step-by-step explanation:

The number of times the bacterial cell is smaller than the amoeba cell is 7 * 10^-1

The given parameters are:

Bacteria cell = 3 x 10^-6 m

Amoeba cell = 4.5 x 10^-4 m

The number of times (n) is calculated as

n = Amoeba cell/Bacteria cell

This gives

n = (3 x 10^-6 m)/(4.5 x 10^-4 m)

This gives

n = 0.7 * 10^-2

Rewrite as

n = 7 * 10^-1

Hence, the number of times the bacterial cell is smaller than the amoeba cell is 7 * 10^-1

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Answer:

The equation in point-slope is [tex]\mathbf{y+5=3(x-6)}[/tex]

Step-by-step explanation:

We need to write the point-slope form of the equation of the line passing through the point (6,-5) and perpendicular to the line [tex]y=-\frac{1}{3}x+4[/tex]

The general form of point-slope is; [tex]y-y_1=m(x-x_1)[/tex]

where m is slope and [tex](x_1,y_1)[/tex] is the point

We need to calculate slope.

We are given equation of line [tex]y=-\frac{1}{3}x+4[/tex] that is perpendicular to the required line.

The equation is given in slope-intercept form [tex]y=mx+b[/tex] where m is slope.

Comparing both equations we get m= -1/3

But we know that when lines are perpendicular their slopes are opposite reciprocal of each other i.e [tex]m=-\frac{1}{m}[/tex]

So, slope of required line is m = 3 (opposite reciprocal of -1/3)

Now, the equation in point-slope form having slope m=3 and point (6,-5) is

[tex]y-y_1=m(x-x_1)\\y-(-5)=3(x-6)\\y+5=3(x-6)[/tex]

So, The equation in point-slope is [tex]\mathbf{y+5=3(x-6)}[/tex]

Answer:

Step-by-step explanation:

As all edges of a cube are expanding at a rate of 2 centimeters per second.

i.e ds/dt = 2 cm/s

The formula of volume of cube: V = s³

Differentiating the volume:

dv/dt = 3s²

Write ds/dt following derivative of volume

dv/dt = 3s² ds/dt

plug in the value: ds/dt = 2 cm/s

dv/dt = (3s²) (2)

dv/dt = 6s²

Given the edge is 2cm.

so plug in the value: s=2

dv/dt = 6s²

          = 6(2)²=6(4)=24 cm³/per second

SIMILARLY,

When the edge is 14cm

dv/dt = 6s²

plug in the value: s=14

dv/dt = 6s²

         = 6(14)²=6(196)=1176 cm³/per second

Thus,

The volume will be:

(a) 24 cm³

(b) 1176 cm³

Given:

Expanding rate,

Let,

(a)

When,

then,

→ [tex]\frac{dx}{dt} = 2 \ cm/sec[/tex]

Let,

→ [tex]V = x^3[/tex]

→ [tex]\frac{dV}{dt} = 3x^2 \frac{dx}{dt}[/tex]

        [tex]= 3\times 2^2\times 2[/tex]

        [tex]= 3\times 4\times 2[/tex]

        [tex]= 24 \ cm^3[/tex]

(b)

When,

then,

→ [tex]\frac{dx}{dt} = 2 \ cm/sec[/tex]

Let,

→ [tex]V = x^3[/tex]

→ [tex]\frac{dV}{dt} = 3x^2 \frac{dx}{dt}[/tex]

        [tex]=3\times 14^2\times 2[/tex]

        [tex]= 1176 \ cm^3[/tex]

Thus the above answer is correct.

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Answer:

x = ½

y = 3

Step-by-step explanation:

0,8 –4x = –0,4y ==> –4x + 0,4y = –0,8

6x + 0,4y = 4,2 ==> 6x + 0,4y = 4,2

______________–

–10x = –5,0

x = –5/–10

x = 1/2

–4x + 0,4y = –0,8

–4(½) + 0,4y = –0,8

–2 + 0,4y = –0,8

0,4y = –0,8 + 2

y = 1,2/0,4

y = 3

x = ½

y = 3

Follow my account^^

Answer:

94

Step-by-step explanation:

Answer:

T<5,-2>

Step-by-step explanation:

It goes to the the right 5 and down 2 but it is put in a proper format

Answer: The reason why the narrator throw the umbrella down the sewer after the car accident is that the umbrella symbolized the rejection of her mother The narrator feel ashamed about her working mother who cannot afford her the standard of living like she's seen in her friends. in the end, she feel ashamed of this and the umbrella remind her of her shameful thought about her mother

Step-by-step explanation:

Answer:

At first, she was upset. She had seen how Eugenie Roberts’s mother acted to her child and how she had treated them, with kindness and utmost interest. She was jealous because her mother had been working all of the time. After her mother came to pick them up, she told her mother she wanted her to quit her job, she didn't want her to work, she wanted to feel like every kid and have her mother there with her to let her know she loved her. And then she had gotten into an accident, in her anger, her mother tilted her head back and closed her eyes, waiting for the yelling people to approach her car. But she thought her mother was dead, she screamed at her mother to open her eyes, before her mother told her to be quiet because people were already going to yell at her and she couldn't take any more yelling. She threw her umbrella in the sewer. Deciding to never be that angry with her mother, for working again.

I hope this helps! :)

Answer: B. ZX is parallel to CA

Step-by-step explanation:

B is the correct answer because ZX and CA form parallel lines which shows they are parallel to each other.

Answer:

h'(t)= -12

Step-by-step explanation:

h'(t)=d/dt (-6t x 2 + 24 + 6)

h'(t)=d/dt (-12t + 24 + 6)

h'(t)=d/dt (-12t + 30)

h'(t)=d/dt (-12t) + d/dt (30)

h'(t)= -12+0

a) After 2 seconds the rock will be 30 feet above the surface.

b) After 3.83, 0.17 seconds the rock will be 10 feet above the surface.

a) Given that the height = h(t) =30

Plug it in the equation and find t.

[tex]30=-6t^2+24t+6\\6t^2-24t+24=0\\6(t^2-4t+4)=0\\6(t-2)^2=0\\t=2[/tex]

b) Given that the height = h(t) =10

Plug it in the equation and find t.

[tex]10=-6t^2+24t+6\\6t^2-24t+4=0\\2(3t^2-12t+2)=0\\3t^2-12t+2=0[/tex]

Then use the quadratic formula.

[tex]t=\frac{12 \pm \sqrt{(-12)^2-4(3)(2)} }{2(3)}\\ t=\frac{12 \pm \sqrt{120} }{6}\\\\t=3.83, 0.17[/tex]

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Answer: D) No; If x is 5, the expression on the left simplifies to 8, making the inequality false.

In other words, if x = 5, then x+3 becomes 5+3 which ultimately becomes 8, but this is not greater than 8 on the right side.

Your steps could look like this

x+3 > 8

5+3 > 8 ... replace x with 5

8 > 8 ... this is a false inequality

Answer:

no solution

Step-by-step explanation:

solve the equation

3x - 8 = 3(x-4) + 1    

3x - 8 = 3x - 11

3x + 3 = 3x

x + 3 = x

A number x plus 3 cannot equal a number x.        

the given equation has no solutions.

The equation 3x - 8 = 3(x - 4) + 1 is a linear equation. To determine the number of solutions, we can simplify and analyze the equation.

Expanding the right side of the equation, we have 3x - 8 = 3x - 12 + 1.

Simplifying further, we get 3x - 8 = 3x - 11.

By subtracting 3x from both sides, we have -8 = -11.

However, this leads to a contradiction. -8 is not equal to -11.

Since the equation leads to a contradiction, there is no solution to the equation.

In conclusion, the given equation has no solutions.

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Answer: either 14

Step-by-step explanation:

The altitude of the airplane after it descends is 13,409 feet.

The meaning of ALTITUDE is the vertical elevation of an object above a surface (such as sea level or land) of a planet or natural satellite.

Now it is given that,

Initial Altitude of airplane = 14,382 feet

Then plane ascends = 9,372 feet

So, Altitude of airplane = 14,382 feet + 9,372 feet = 23,754 feet

Again airplane descends = 10,345 feet

So, Altitude of airplane = 23,754 feet - 10,345 feet

⇒ Altitude of airplane = 13,409 feet

Thus, the altitude of the airplane after it descends is 13,409 feet.

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The given trigonometry proof is given below

(a)[tex]\frac{1}{1+\sin (\theta)}+\frac{1}{1-\sin (\theta)}=2 \sec ^2(\theta)[/tex]

Manipulating left side

[tex]$$\begin{aligned}&\frac{1}{1+\sin (\theta)}+\frac{1}{1-\sin (\theta)} \\&\text { Simplify } \frac{1}{1+\sin (\theta)}+\frac{1}{1-\sin (\theta)}: \frac{2}{(\sin (\theta)+1)(-\sin (\theta)+1)} \\&=\frac{2}{(1+\sin (\theta))(1-\sin (\theta))}\end{aligned}$$[/tex]

Rewrite using trig identities

[tex]=\frac{2}{\cos ^2(\theta)}[/tex]

Use the basic trigonometric identity: [tex]\frac{1}{\cos (x)}=\sec (x)[/tex]

[tex]$$=2 \sec ^2(\theta)$$[/tex]

(b)[tex]\frac{\cos (x)}{1+\sin (x)}=\sec (x)-\tan (x)[/tex]

Manipulating right side

[tex]$$\sec (x)-\tan (x)$$[/tex]

Express with sin, cos

[tex]=\frac{1-\sin (x)}{\cos (x)}[/tex]

Rewrite using trig identities

[tex]=\frac{\cos (x)}{1+\sin (x)}[/tex]

(c)Manipulating right side[tex]$\tan (x)-\cot (x)$[/tex]

Express with sin, [tex]$\cos$[/tex]

[tex]$$\begin{aligned}&=\frac{-\cos ^2(x)+\sin ^2(x)}{\cos (x) \sin (x)} \\&\sin ^2(x)=1-\cos ^2(x) \\&=\frac{1-\cos ^2(x)-\cos ^2(x)}{\cos (x) \sin (x)} \\&=\frac{1-2 \cos ^2(x)}{\sin (x) \cos (x)}\end{aligned}$$[/tex]

(d) [tex]\frac{\sin (x)}{1-\cot (x)}+\frac{\cos (x)}{1-\tan (x)}=\sin (x)+\cos (x)[/tex]

Manipulating left side

[tex]\frac{\sin (x)}{1-\cot (x)}+\frac{\cos (x)}{1-\tan (x)}[/tex]

Express with sin, cos

[tex]=\cos (x)+\sin (x)[/tex]

(e)Manipulating left side

[tex]\frac{2-\sec ^2(x)}{\sec ^2(x)+2 \tan (x)}[/tex]

Express with sin, cos

[tex]=\frac{-1+2 \cos ^2(x)}{1+2 \cos (x) \sin (x)}$$[/tex]

Rewrite using trig identities

[tex]=\frac{\cos (x)-\sin (x)}{\cos (x)+\sin (x)}$$[/tex]

(f)Manipulating left side [tex]$\cot ^2(x)-\cot ^2(y)$[/tex]

Express with sin, cos

[tex]=\frac{\cos ^2(x) \sin ^2(y)-\cos ^2(y) \sin ^2(x)}{\sin ^2(x) \sin ^2(y)}$$[/tex]

Rewrite using trig identities

[tex]=\frac{\cos ^2(x)-\cos ^2(y)}{\sin ^2(x) \sin ^2(y)}$$[/tex]

Trigonometry is the field of mathematics that deals with certain angles' functions and how to use such functions in computations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.

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Answer:

C. Graph B

Step-by-step explanation:

y ≥ 2x + 3

y ≤ -2x - 4

To find which side of the line the answer is, we can set y and x to 0 and see if the equation is true or false (this only works if the cordance of (0,0) does not lie on the line)

0 ≥ 2(0) + 3

0 ≥ 3 FALSE (the side of the line that should be shaded is the one that does not include the cordance of (0,0))

0 ≤ -2(0) - 4

0 ≤ - 4 FALSE (the side of the line that should be shaded is the one that does not include the cordance of (0,0))

Answer:

one spool of thread costs $1.89

Step-by-step explanation:

$8.99x3=$26.97

$32.64-$26.97=$5.76

$5.76 divided by 3=$1.89

Answer:

12π

Step-by-step explanation:

The formula for arc length is given as:

[tex] s = \frac{\theta}{360\degree} \times 2\pi r[/tex]

Plug r = 24 and θ=π/2 in the above formula, we fi d:

[tex] s = \frac{\frac{\pi}{2}}{360\degree} \times 2\pi \times 24\\\\

s = \frac{\frac{\pi}{2}}{2 \pi} \times 48\pi\\\\

s = \frac{\pi}{2\times 2 \pi} \times 48\pi \\\\

s = \frac{\pi}{4\pi} \times 48\pi \\\\

\huge \purple {\boxed{s = 12\pi}} \\

[/tex]

Step-by-step explanation:

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Two standards $6$-sided dice are rolled. The probability that the sum rolled is a perfect square 7/36.

Likelihood is the part of math concerning mathematical portrayals of how likely an occasion is to happen, or how likely it is that a suggestion is valid. Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a recommendation is valid. Likelihood and measurements, the parts of science worried about the regulations administering arbitrary occasions, including the assortment, investigation, understanding, and show of mathematical information. While calculation and variable based math were concentrated on by old Greek mathematicians over long time back, the ideas of likelihood just arose in the seventeenth and eighteenth 100 years.

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Answer:

C.) 120 or Option C is incorrect.

The answer is B.) 110

Step-by-step explanation:

See screenshot below

Hope this helps!

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