if you horizontally strech the quadratic parent function, f(x)=x^2, by a factor of 4, what is the equation of the new function?

Answer:

[tex]3 -\sqrt[2]3[/tex]

Step-by-step explanation:

Given

[tex]\frac{2\sqrt[3]{9}}{1 + \sqrt[3]{3} + \sqrt[3]{9}}[/tex]

Required

Simplify

Rewrite the given expression in index form

[tex]\frac{2 * 9 ^\frac{1}{3}}{1 + 3^{\frac{1}{3}} + 9^{\frac{1}{3}}}[/tex]

Express 9 as 3²

[tex]\frac{2 * 3^2^*^\frac{1}{3}}{1 + 3^{\frac{1}{3}} + 3^2^*^{\frac{1}{3}}}[/tex]

[tex]\frac{2 * 3^\frac{2}{3}}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}}[/tex]

Multiply the numerator and denominator by [tex]1 - 3^{\frac{1}{3}}[/tex]

[tex]\frac{2 * 3^\frac{2}{3}}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}} * \frac{1 - 3^{\frac{1}{3}}}{1 - 3^{\frac{1}{3}}}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) (1 - 3^{\frac{1}{3}})}{(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})(1 - 3^{\frac{1}{3}})}[/tex]

Open the bracket

[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{2}{3})(3^{\frac{1}{3}})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]

Simplify the Numerator using Laws of Indices

[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{2+1}{3})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]

Further Simplify

[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{3}{3})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3^1)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]

Simplify the denominator

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - (3^{\frac{1}{3}})(3^{\frac{1}{3}}) - (3^{\frac{1}{3}})(3^{\frac{2}{3}})}[/tex]

Further Simplify Using Laws of Indices

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - (3^{\frac{1+1}{3}}) - (3^{\frac{1+2}{3}})}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3^{\frac{3}{3}}}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3^1}}[/tex]

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3}}[/tex]

Collect Like Terms

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 - 3+ 3^{\frac{1}{3}} - 3^{\frac{1}{3}}+ 3^{\frac{2}{3}} - 3^{\frac{2}{3}} }}[/tex]

Group Like Terms for Clarity

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{(1 - 3) + (3^{\frac{1}{3}} - 3^{\frac{1}{3}}) + (3^{\frac{2}{3}} - 3^{\frac{2}{3}} )}}[/tex]

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

[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{-2}}[/tex]

Divide the fraction

[tex]-(3^\frac{2}{3}) + (3)[/tex]

Reorder the above expression

[tex]3 -3^\frac{2}{3}[/tex]

The expression can be represented as

[tex]3 -\sqrt[2]3[/tex]

Hence;

[tex]\frac{2\sqrt[3]{9}}{1 + \sqrt[3]{3} + \sqrt[3]{9}}[/tex] when simplified is equivalent to [tex]3 -\sqrt[2]3[/tex]

Answer:

The shortest altitude = 8 cm

Step-by-step explanation:

Where we have the sides given by

15 cm, 17 cm, 8 cm

From cosine rule, we have;

a² = b² + c² - 2×b×c×cos(A)

We have

For the side 15 cm,

15² = 17² + 8² - 2×17×8 cos A

-388 = -612×cos×A

A = 61.93°

17² = 15² + 8² - 2×15×8 ×cos B

0 = -240·cos B

B = 90°

Therefore, 17 is the hypotenuse side and 15 and 8 are the legs, either of which can be the height which gives the shortest altitude as 8 cm

Answer:

38.5°

Step-by-step explanation:

Given that the height of the building is 8 yard and the distance between Jonathan and the building is 10 yards.

The sun is at the top of the building, let the distance between Jonathan laying on the ground and the top of the building be x. Using Pythagoras:

x² = 10² + 8²

x² = 100 + 64

x² = 164

x = √164 = 12.86 yards

For a triangle with sides a, b, c and their respective opposite angles A, B, and C. The sine rule is given as:

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Let the angle that the sunlight hit the ground be y°. The andle between the building and the ground is 90°. Therefore using sine rule:

[tex]\frac{8}{sin(y)}=\frac{12.86}{sin(90)}\\\\sin(y)=\frac{8*sin(90)}{12.86}\\\\sin(y)=0.622\\\\y=sin^{-1}0.622\\\\y = 38.5^0[/tex]

Answer:

The correct option is;

y minus x = negative 4

(y - x = -4)

Step-by-step explanation:

Given that the line y  = x - 4 of the graph passes through the points (0, -4) and (4, 0)

Comparing with the general equation of a straight line, y = m·x + c, where m is the slope and c is the y-intercept gives;

The slope of the equation y = x - 4 = 1

The y-intercept of the equation y = x - 4 = -4

Two equations will have an infinite number of solutions when they are on the same line, that is having the same slope and intercept, we check for the slope and the intercept of the given options as follows;

For y - x = -4, we have;

y = x - 4 which is the same as the given equation and both equations will have an infinite number of solutions

For y - x = -2 we have;

y = x - 2

The slope is the same as the given equation but the intercept is different giving no solution

For y - 4 = x, we have;

y = x + 4

The slope is the same as the given equation but the intercept is different giving no solution

For y + 4x = 1, we have;

y = 1 - 4x

The slope and  intercept are different giving one solution.

Answer:

y - x = -4

Step-by-step explanation:

Answer:

12 weeks

Step-by-step explanation:

To solve this, all you need to do is divided 24 pieces by the two he learns per week. You'll then find it will take him 12 weeks

Answer:

2, 3 , 5, 7

Step-by-step explanation:

2(x - 2)/3 < (x + 1)/2 < 3(5x + 6)/4

Considering:

    2(x - 2)/3 < (x + 1)/2

<=>(2x - 4)/3 < (x + 1)/2

<=> (2x - 4)*2 < (x + 1)*3

<=> 4x - 8 < 3x + 3

<=> 4x - 3x < 8 + 3

<=> x < 11

Considering:

     (x + 1)/2 < 3(5x + 6)/4

<=>(x + 1)/2 < (15x + 18)/4

<=>(x + 1)*4 < (15x + 18)*2

<=> 4x + 4 < 30x + 36

<=> 4x - 30x < 36 - 4

<=> -26x < 32

<=> 26x > -32

<=> x > -32/26

=> -32/26 < x < 11

The prime numbers satisfy the above inequalities: 2, 3 , 5, 7

Answer: Griffin charge $79.854 to his credit card when he bought the sneakers.

Step-by-step explanation:

Griffin ordered a pair of sneakers online.

Value of each credit point = 1 cent

Then , value of 16 credit points = 16 cents = $0.16 [1$ = 100 cents]

Cost of shoes = Rs $80

Charge to credit card = (Cost of shoes) - (Value of 16 credit points)

= $(80-0.16)

= $79.84

Hence, Griffin charge $79.854 to his credit card when he bought the sneakers.

Answer:

Igloo Ice has the lowest delivery charge.

Step-by-step explanation:

Igloo Ice when you plug in 120 for the y you get 25.714 as the x.

Freds freeze at 120 is 20.

And lastly Tasty treats at 120 is 24, so Igloo Ice has the lowest delivery charge per person (you pay $120 for 25.714 people.)

Answer:

Igloo Ice

Step-by-step explanation:

Igloo Ice C(n) = 1.75n + 75

Fred's Freeze C(n) = 2n + 80

Tasty Treats C(n) = 1.25n + 90

75 is the lowest delivery charge

C(n) is total charge including what they are delivering

Answer:

? = 23

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan ? = opp/ adj

tan ? = 3/7

take the inverse tan of each side

tan ^-1 tan ? = tan ^-1 ( 3/7)

? = 23.19859051

To the nearest degree

? = 23

Answer:

h = V3B

Step-by-step explanation:

V = 1/3B · h

Divide volume by 1/3 B to get h by itself

V/1/3B = V3B

Answer:

39858075

Step-by-step explanation:

Hello,

One basic way to see it is to compute the values.

   75 = 25 * 3

   225 = 75 * 3

   675 = 225 * 3

   etc ...

We can notice that this is multiplied by 3 every 10 years so we can compute as below.

year         population

1970 25

1980 75

1990 225

2000 675

2010 2025

2020 6075

2030 18225

2040 54675

2050 164025

2060 492075

2070 1476225

2080 4428675

2090 13286025

2100 39858075

So the correct answer is 39858075

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

22

Step-by-step explanation:

Since the mean of the set is 11, the sum of the integers in the set must be 11 * 5 = 55. The median must be the 3rd integer, therefore the 3rd integer is 9. Since 9 > 7 and there are only 2 integers less than the median, the 1st and 2nd integers must be 7 and 7 because 7 is the mode. This leaves the last two integers to have a sum of 55 - (9 + 7 + 7) = 32. In order for the last integer (the greatest one) to have the largest value, the fourth integer must be as small as possible. Therefore, the fourth integer is 10 (it can't be 9 because 7 is the only mode) which makes the answer 32 - 10 = 22.

Answer:

15

Step-by-step explanation:

Answer:

21.213

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

f(x)=-x^2+6x+1

This is a parabola that opens downward( the - coefficient of x^2)

The maximumx is at the vertex

The x coordinate is at

-b/2a  where ax^2 + bx +c  a =-1  b=6 c=1

-6/(2*-1)

-6/-2 = 3

The x coordinate of the vertex is 3

f(3) = - (3)^2 +6(3)=1

    = -9+18+1

    = 10

The vertex is ( 3,10)

The maximum value is 10

Answer:

[tex]10[/tex]

Step-by-step explanation:

[tex]f(x)=-x^2+6x+1[/tex]

x coordinate:

[tex]\frac{-b}{2a}[/tex]

[tex]a=-1\\b=6[/tex]

[tex]\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3[/tex]

y-coordinate:

[tex]f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10[/tex]

Answer:

5

Step-by-step explanation:

The initial value is when x=0

When x=0, y =5

The initial value is 5

Answer:

A) the probability of winning is 0.24%.

B) Yes i will play the game

C) Despite the fact that the probability of winning is very low, one should play the game because the expected value of the game is positive.

Step-by-step explanation:

Expected value of X is denoted by;

E(X) = x1•p1 + x2•p2 +..... xn•pn

Where;

xi is the observation and pi is the probability of xi

Now, let's make p the probability of the winning bet and 1 - p be the probability of losing the game

If the bet is win, the net gain is $98,800 and if the bet is lose, the loss is -$1200.

Hence the probability distribution will be;

For xi = $98,800, pi = p

For xi = -$1,200, pi = 1 - p

So;

E(X) = Σxi.pi

Thus;

1200 = 98800p - 1200(1 - p)

1200 = 98800p - 1200 + 1200p

1200 + 1200 = 100000p

2400 = 100000p

p = 2400/100000

p = 0.024

Thus, the probability of winning is 0.24%.

Despite the fact that the probability of winning is very low, one should play the game because the expected value of the game is positive.

Answer:

1.26 * 10 ^6

Step-by-step explanation:

1260000

Scientific notation is of the form a* 10 ^b

where a is a number between 1 and less than 10

Move the decimal 6 places to the left

1.26 ( dropping the extra zeros)

b = +6 since we moved the decimal 6 places)

1.26 * 10 ^6

The number 1260000 in scientific notation is 1.26 x [tex]10^6[/tex].

We have,

1260000

Write the zeroes in powers of 10.

Write a number between 1 to 10 along with the power of 10.

Now,

126 x 10000

This can be written as,

126 x [tex]10^4[/tex]

Now,

126 can be written as 126/100 x 100.

i.e

1.26 x 100 or 1.26 x 10²

Now,

1.26 x 10² x [tex]10^4[/tex]

1.26 x [tex]10^{2 + 4}[/tex]

1.26 x [tex]10^6[/tex]

Thus,

The number 1260000 in scientific notation is 1.26 x [tex]10^6[/tex].

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Answer: 380

Step-by-step explanation:

Total number of players = 20

To select a captain and a vice captain :

One captain from a total of 20 players :

20 combination 1 = 20C1 = 20 ways

Total number of players left after selecting a captain = 20 - 1 = 19

Number of players left from which to select a vice captain = 19

Therefore, one vice captain from a group of 19 players :

19 combination 1 = 19C1 = 19 ways

Therefore no of different possible ways to select a captain and a vice captain :

20C1 × 19C1 = 20 × 19 = 380 Ways

Answer:

  D.  y = f(x/-1)

Step-by-step explanation:

The function f(x) is reflected across the y-axis to make the red graph. Such a reflection is accomplished by a horizontal scale factor of -1.

For some horizontal scale factor k, the transformed function is ...

  y = f(x/k)

Here, we have k = -1, so the transformed function is ...

  y = f(x/-1)

Answer:

1.33,3.667

Step-by-step explanation:

Use y=mx+b for second system

which is y=5/2x+7

Now use substitution,graph, or elimination method.

Answer:

44 degrees

Step-by-step explanation:

Since MN is a tangent, it forms a right angle wheng it intersects line MP since MP is the diameter. So, 90+46 is 136 and since there are 180 degrees in a traingle, 180-136 is 44.

Hope this is helpful! :)

The answer is 44 degrees.

:D

Answer:

Step-by-step explanation:

In triangle DEF, we have:

Given:

<EDF=56

<EFD=84

So, <DEF =180 - 56 - 84 =40 (sum of triangle angles is 180)

____________

DE is a midsegment of triangle ACB

( since CD=DA(given)=>D is midpoint of [CD]

and BE = EA => E midpoint of [BA] )

According to midsegment Theorem,

(DE) // (CB) "//"means parallel

and DE = CB/2 = FB =CF

___________

DEBF is a parm /parallelogram.

Proof: (DE) // (FB) ( (DE) // (CB))

AND DE = FB

Then, <EBF = <EDF = 56

___________

DEFC is parm.

Proof: (DE) // (CF) ((DE) // (CB))

And DE = CF

Therefore, <DCF = <DEF =40

___________

In triangle ACB, we have:

<CAB =180 - <ACB - <ABC =180 - 40 - 56 =84(sum of triangle angles is 180)

[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK! [/tex]

Answer:

The value of t that will satisfy the equation is π/6 (which is 30 degrees)

Step-by-step explanation:

The function that models the movement of the particle is given as;

S(t) = 2 sin(t) + 3 cos (t)

Now we want to the value of t between 0 and pi/2 that satisfies the equation;

s(t) = (2+ 3√3)/2 = 1 + 3√3/2

What we do here is simply find that value of t that would ensure that;

2sin(t) + 3cos(t) = 1 + 3√3/2

Without any need for rigorous calculations, this value of t can be gotten by inspection.

From our regular trigonometry, we know that the sin of angle 30 is 1/2 and its cos value is √3/2

We can make a substitution for it in this equation.

We obtain the following;

2 sin(30) + 3cos (30) and that is exactly equal to 1 + 3√3/2

Do not forget however that we have a range. And the range in question is between 0 and π/2

Kindly that π/2 in degrees is 90 degrees

So our range of values here is between 0 and 90 degrees.

So to follow the notation in the question, the value within the range that will satisfy the equation is π/6

The equation of line which is perpendicular to the line FG is

y = -2x -3.

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

[tex](y -y_{1}) = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } (x-x_{1} )[/tex]

If [tex]m_{1}[/tex] be the slope of one line, then the slope of the perpendicular line is [tex]\frac{-1}{m_{1} }[/tex].

The slope intercept form of the line is given by  y = mx + b

Where, m is the slope of a line.

According to the given question

We have a line FG and the coordinates of points F and G are (-5,1) and (9,8) respectively.

Therefore, the slope of the line FG = [tex]\frac{8-1}{9+5}=\frac{7}{14} =\frac{1}{2}[/tex]

⇒ The slope of the line which is parallel to line FG is -2

Now, from the given option of the equation of line , y = -2x -3 has a slope of -2 .

Hence, the equation of line which is perpendicular to the line FG is

y = -2x -3.

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Answer: B

Step-by-step explanation:

A center angle is an angle that has rays that originate from the center.

Answer:

2√2

Step-by-step explanation:

By simplifying we get the value is [tex]2\sqrt{2}[/tex]

The combination in which numbers, variables, functions are present, is called expression.

Example : 6y-3x+2, 2y-3 etc.

The given expression is [tex]\frac{1}{\sqrt{2}+1 } +\frac{1}{\sqrt{2}-1 }[/tex]

Simplifying,

First we take the LCM of [tex]\sqrt{2}+1[/tex] & [tex]\sqrt{2}-1[/tex]

Then expression becomes, [tex]\frac{(\sqrt{2}-1)-(\sqrt{2}+1) }{(\sqrt{2}+1)(\sqrt{2}-1)}[/tex]

Now, using [tex](a+b)(a-b)=a^{2}- b^{2}[/tex] we get, [tex]\frac{\sqrt{2}-1+\sqrt{2}+1 }{(\sqrt{2}) ^{2} - 1^{2} }[/tex]

Now, simplifying, we get,  [tex]\frac{2\sqrt{2} }{2-1}[/tex] = [tex]2\sqrt{2}[/tex]

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Answer:

c

Step-by-step explanation:

the answer is c becuase i know this que

Answer:

All

Step-by-step explanation:

We can check it by using the Pythagorean theorem.

[tex]a {}^{2} + b {}^{2} = c {}^{2} = {3}^{2} + { \sqrt{27} }^{2} = 6 {}^{2} = 9 + 27 = 36 = 36 = 36 [/tex]

[tex] {a}^{2} + {b}^{2} = c {}^{2} = {8}^{2} + {15}^{2} = {17}^{2} = 64 + 225 = 289 = 289 = 289[/tex]

[tex]a {}^{2} + b {}^{2} = c {}^{2} = 5 {}^{2} + {5}^{2} = { \sqrt{50} }^{2} = 25 + 25 = 50 = 50 = 50 = [/tex]

Hope this helps ;) ❤❤❤

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope( gradient ) and y the y- intercept )

The 3 equations are in this form

(1)

y = 2x + 3

with gradient = 2 and y- intercept = 3

(2)

y = 5x + 1

with gradient = 5 and y- intercept = 1

(3)

y = 3x + 2

with gradient = 3 and y- intercept = 2

Answer:

Below

Step-by-step explanation:

● a^(-2) *b^3

●(1/a^2) *b^3

● b^3 / a^2