Given the function f(x)= x^2-7 and g(x) = 2x-x^3 what is the value of f(g(2))

Answer:

  5.6

Step-by-step explanation:

We assume that 7 is the measure of the portion of the secant that is inside the circle between the circle and the intersection with the other chord.

The product of segment lengths on the same chord is a constant for chords that intersect at the same point. That is, ...

  10x = 8·7

  x = 56/10

  x = 5.6

_____

Comment on the geometry

If you draw the figure to scale, you find the geometry shown is impossible. The arc measures and chord lengths are incompatible.

Answer:

  3.33×10⁴

Step-by-step explanation:

You can use the hint, or you can use a common exponent. Here is the latter case.

  (3.9×10⁴) -(5.7×10³) = (3.9×10⁴) -(0.57×10⁴) = (3.9 -0.57)×10⁴

  = 3.33×10⁴

_____

With a little practice, you can see the effect on exponents of moving the decimal point. Here, we have ...

  5.7×10³ = (0.57×10)×10³ = 0.57×(10×10³) = 0.57×10⁴

__

When adding or subtracting in scientific notation, all that is required is that the exponents of all the numbers be the same. The hint says make all the exponents be 0. Above, we have chosen to make them all be 4. You could also use 3:

  (3.9×10⁴) -(5.7×10³) = (39×10³) -(5.7×10³) = (39 -5.7)×10³

  = 33.3×10³ = 3.33×10⁴

Answer:

31/256

Step-by-step explanation:

0.12109375 = 12109375/100000000

= 31/256

Dividing numerator and denominator by 390625.. we have the simplest solution

You can start out by dividing by 5 the numerator and denominator.you would see this division by 5 goes on 8 times

Or you can start out dividing both numerator and denominator by 25, we see this division goes on 4 times

Answer:

Step-by-step explanation:

0.12109375

=[tex]=\frac{12109375}{100,000,000} \\=\frac{484375}{4,000,000} \\=\frac{19375}{160000} \\=\frac{775}{6400} \\=\frac{31}{256}[/tex]

Answer:

(6x)*(4x^7) = (6*4)*(x*x^7) = 24*x^8

(6x)*(4x^7) = 24*x^7 is wrong in calculation of x

Hope this helps!

:)

Answer:

Nothing is wrong with it

x= 1

Step-by-step explanation:

It has a solution; here is the solution.

(6x)(4x^7) = 24 x^ 7

x * 24x^7= 24x^7

x = 24x^7 / 24x^7

x = 1

Answer:

cone, [tex]\frac{1}{3}[/tex] , [tex]\frac{1}{3} \pi r^{2}h[/tex] , [tex]\pi r^{2}[/tex], base, h, height, same, [tex]\frac{1}{3}[/tex] , [tex]\frac{1}{3}[/tex] , 3

Step-by-step explanation:

The volume of a cone is equal to [tex]\frac{1}{3}[/tex] the volume of a cylinder that has the same base and height. The formula for the volume of a cone is [tex]\frac{1}{3}\pi r^{2}h[/tex].  stands for the area of the base and h is the height of the cone. Knowing this, we could quickly find the volume of a cone that has the same base and height as a cylinder with a volume of 9 cubic cm. Since the volume of a cone is [tex]\frac{1}{3}[/tex] the volume of a cylinder (with the same base and height), we would multiply 9*[tex]\frac{1}{3}[/tex] to obtain a volume of 3 cubic cm.

Answer:

  a) Megan's total so far is 3 km more than necessary for an average of 15 km

  b) 22 km

Step-by-step explanation:

a) The total of differences from 15 is ...

  -1 + 8 + (-2) +(-2) = 3

Since this is more than 0, Megan's average is more than 15.

__

b) The total of differences from 17 is ...

  -3 +6 -4 -4 = -5

To increase her average to 17 km, Megan must walk 17+5 = 22 km on Friday.

_____

Comment on the approach

In general, I find it easier mentally to deal with small numbers than with larger ones. So adding small differences can be easier than computing larger sums.

a) By computing the difference from the supposed average, we have effectively found the difference of the sum of values from the total necessary to give the required average. That is, Megan's average would be 15 if her total distance were 4·15 = 60. Her total distance is (4·15 +3) = 63, so her average is more than 15.

b) By finding out how much the total is below that necessary for the desired average, we determine the amount above that average the final number needs to be.

  (14 -17) +(23 -17) +(13 -17) +(13 -17) +(Friday -17) = 0 . . . . the Friday value to make an average of 17

  14 +23 +13 +13 +Friday = 5·17 . . . . . . . add 5·17

  (14 +23 +13 +13 +Friday)/5 = 17 . . . . . . shows the Friday amount gives the required average

  Friday = 17 -((14 -17) +(23 -17) +(13 -17) +(13 -17)) . . . . first equation rearranged to show how we computed Friday

  Friday = 17 -(-5) = 17 +5 = 22

Answer:

4096 horses, or 4 to the power of 6

Step-by-step explanation:

(4²)³×4 to the power of 0

We simplify the equation,

(16)³×4 to the power of 0

4096×1 (Since 4 to the power of 0 is 1)

= 4096 horses on the farm which is 4 to the power of 6

- Hope this helps!

Answer:

26.00 + 2x = y           14.00 + 4x = y

Step-by-step explanation:

depending on the amount of people in the car determines numbers of the equation so variables had to be placed instead.

Answer:

The experimental probability of tossing heads is

[tex]\frac{8}{20}=\frac{(8 \div 4)}{(20 \div4)} = \boxed{\frac{2}{5} } ✓ \\ [/tex]

Answer:

It’s only sequence A I think

Step-by-step explanation:

I hope this was helpful

Answer:

Sequence A

Step-by-step explanation:

Answer:

0.982 mile

Step-by-step explanation:

1 mile = 5280 ft

h = (5183ft) *(1 mile/5280ft) = 0.982 miles

The height of Denver, Colorado above sea level rounded to three decimal places is 0.982miles.

Measurement is simply the process of associating numbers with physical quantities and events.

Converting measurements in foot to miles as;

1foot = (1/5280)miles

Given that;

Since 1foot = (1/5280)miles

5183ft = ( 5183 / 5280 )miles

5183ft = 0.982miles

Therefore, the height of Denver, Colorado above sea level rounded to three decimal places is 0.982miles.

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Answer:

408cm

Step-by-step explanation:

U got this

The total surface area of the triangular prism is 14 cm². Then the correct option is B.

A triangular prism is a closed solid that has two parallel triangular bases connected by a rectangular surface.

The total surface area of the triangular prism will be

[tex]\rm Total\ area = 3(area \ of\ rectangle) + 2(area\ of \ triangle)[/tex]

The area of the triangle will be

[tex]\rm area\ of \ triangle = \dfrac{1}{2} * 2 * 4\\\\area\ of \ triangle = 4[/tex]

The area of the rectangle will be

[tex]\rm area\ of \ rectangle = 2 *1\\\\area\ of \ rectangle = 2[/tex]

Then the total area will be

[tex]\rm Total\ area = 2*4 + 3*2\\\\Total\ area = 8 + 6 \\\\Total\ area = 14[/tex]

The total surface area of the triangular prism is 14 cm². Then the correct option is B.

More about the triangular prism link is given below.

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Answer:

  f(m) = 0.128m

Step-by-step explanation:

cost per mile = (cost per gallon)/(miles per gallon) = $3.20/25 = $0.128

Then the desired function is ...

  f(m) = 0.128m

Answer:

I graphed all of the equations on the graph below.

Step-by-step explanation:

At the point (6,4), the equation [tex]x+y\ge10[/tex] uses 6 + 4 ≥ 10. Also, the equation [tex]2x+3y\le24[/tex] uses 2(6) + 3(4) ≤ 24.

If this answer is correct, please make me Brainliest!

Answer:

its A !!

Step-by-step explanation:

[tex] - 2 = \dfrac{3x}{5} + 1 | \times 5 \\ - 10 = 3x + 5 \\ - 3x = 15 | \div ( - 3) \\ x = - 5[/tex]

Answer:

The slope is 2

Y-int is -4

Step-by-step explanation:

For the given equation, y=4−2x the slope and y-intercept of the line will be -2 and 4 respectively.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that the equation is"y=4−2xy"

The given equation is of a straight line, A straight line is a combination of endless points joined on both sides of the point. A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

The given in form of a standard equation can be written as,

y=4−2x

y=-2x+4

Comparing the equation we get, the slope of the line as

m= -2

The intercept of the line is,

b= 4

Thus for the given equation, y=4−2x the slope and y-intercept of the line will be -2 and 4 respectively.

The question is incomplete, "the complete question is to find the slope and intercept for the given equation y=4−2xy."

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Answer:

Are you being timed??

Step-by-step explanation:

Answer:

  t ≈ 0.0664731

Step-by-step explanation:

Use the inverse sine function.

  sin(12t) = 141/197

  12t = arcsin(141/197)

  t = arcsin(141/197)/12

  t ≈ 0.0664731 . . . . . . . radians

__

This is the principal value. There are other solutions at values of t that have integer multiples of π/6 added to this. There are also solutions where any of those values is subtracted from π.

_____

In general, angles in math are assumed to be in radians, unless specified otherwise. This angle corresponds to about 3.81°. (In geometry, the usual assumption is that angles are measured in degrees.)

Answer:

The base is 7 and the height is 9.

Step-by-step explanation:

Answer:

The base is 7 and the height is 9.

Step-by-step explanation:

i got it correct on edge

Relax this isn't really that hard. We're given a triangle with coordinates

X(4,4), Y(12,12), Z(4,12)

and we're told to dilate it around the origin by scale factor 1/4.   The origin part makes it easy; this just means we multiply all the coordinates by 1/4.

So our new triangle is

X'(1,1), Y'(3,3), Z'(1,3)

which we plot in red.

Is that third page asking for the lengths?  We have

X'Y' is the hypotenuse of a right triangle with legs 2 and 2, so

|X'Y'| = 2√2

|Y'Z'| is 3-1 = 2

|Z'X'| = 2

The rule is

(x,y) → (x/4, y/4)

Scale factors are used to enlarge or reduce the size of a shape

The coordinates of the dilated triangle are (1,1), (3,3) and (1,3)

The coordinates of the triangle are given as:

[tex]X = (4,4)[/tex]

[tex]Y = (12,12)[/tex]

[tex] Z = (4,12)[/tex]

The scale factor of dilation is given as:

[tex]k=\frac 14[/tex]

The coordinates of the new triangle after dilation are calculated as follows:

[tex]X' = (4,4) \times \frac 14[/tex]

[tex]X' = (1,1)[/tex]

[tex]Y' = (12,12) \times \frac 14[/tex]

[tex]Y' = (3,3)[/tex]

[tex]Z' = (4,12) \times \frac 14[/tex]

[tex]Z' = (1,3)[/tex]

So, the dilation rule is:

[tex](x,y) \to \frac 14(x,y)[/tex]

Hence, the coordinates of the dilated triangle are (1,1), (3,3) and (1,3)

See attachment for the image of the triangle

Read more about dilations at:

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Answer:

The first step to solve the expression is to solve () i.e. (10-7) will be solved first.

Step-by-step explanation:

Any algebraic expression is solved as per BODMAS rule i.e. in the following sequential order (one after the other).

B - Bracket i.e. ()

O - Of

D - Division

M - Multiplication

A - Addition

S - Subtraction

So, as per BODMAS rule, the bracket  i.e. () expression will be solved at first.

Solving the expression:

15 + 20 ÷ (10 – 7) + 12

[tex]\Rightarrow[/tex] 15 + 20 ÷ 3 + 12

[tex]\Rightarrow[/tex] 15 + 6.67 + 12

[tex]\Rightarrow[/tex] 21.67 + 12

[tex]\Rightarrow[/tex] 33.67

Hence, (10-7) will be evaluated first.

Answer:

10-7 will be done first.

Step-by-step explanation:

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

Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11

When the line segment is divided internally in the ration m:n, we use this formula.  That is when the point C lies somewhere between the points A and B. p= (mx₂+nx₁)/(m+n) & q= (my₂+ny₁)/(m+n)

Given here,  point B on AC Such that the ratio of AB to AC is 5:6

Let the point B(p,q) internally divide the line joining points A(x₁, y₁) and C(x₂, y₂) in the ratio m : n , then,

p= (mx₂+nx₁)/(m+n)

q= (my₂+ny₁)/(m+n)

Here. m=5 and n=6

p=(5x₂+6x₁)/11 , q=(5y₂+6y₁)/11

Hence, Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11

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Answer:

2(x - [tex]\frac{7}{4}[/tex] )² - [tex]\frac{9}{8}[/tex]

Step-by-step explanation:

Given

2x² - 7x + 5

The coefficient of the x² term must be 1, thus factor out 2 from 2x² - 7x

= 2(x² - [tex]\frac{7}{2}[/tex] x ) + 5

To complete the square

add/ subtract ( half the coefficient of the x- term )² to x² - [tex]\frac{7}{2}[/tex] x

= 2(x² + 2(- [tex]\frac{7}{4}[/tex] )x + [tex]\frac{49}{16}[/tex] - [tex]\frac{49}{16}[/tex] ) + 5

= 2(x - [tex]\frac{7}{4}[/tex] )² - [tex]\frac{98}{16}[/tex] + 5

= 2(x - [tex]\frac{7}{4}[/tex] )² - [tex]\frac{18}{16}[/tex]

= 2(x - [tex]\frac{7}{4}[/tex] )² - [tex]\frac{9}{8}[/tex]

Answer:

g(x) = 2(x - 1.75)^2 - 1.125.

Step-by-step explanation:

g(x) = 2x^2 – 7x + 5

First take the 2 out of the first  terms:

g(x) = 2(x^2 - 3.5x) + 5

Now complete the square on the expression in the parentheses:

g(x) = 2 [ (x - 1.75)^2 - 1.75^2] + 5

g(x) = 2 [ (x - 1.75)^2 - 3.0625] + 5

g(x) = 2(x - 1.75)^2 - 6.125 + 5

g(x) = 2(x - 1.75)^2 - 1.125.

Answer:2

Step-by-step explanation:

So they are both equal right. They gave us what a is which was 2 so that means b must be 2 as well.

Hope I helped

Answer:

2

Step-by-step explanation:

The slope of line b is also 2 as they are parallel to eachother and parallel lines have equal slopes.

Answer:

  see below

Step-by-step explanation:

Corresponding letters (vertices) are in the same order in the similarity statement. That is, if L is the first letter in ∆LMN, then it corresponds to the first letter (R) in ∆RST. That is the meaning of ∆LMN ~ ∆RST.

3. Everywhere you see L, replace it with R.

  Everywhere you see M, replace it with S.

  Everywhere you see N, replace it with T.

This goes for both segments and angles.

__

4. Everywhere you see A, replace it with H.

  Everywhere you see B, replace it with G.

  Everywhere you see C, replace it with F.

  Everywhere you see D, replace it with E.

This goes for both segments and angles.

Answer: 0 represents he stays in the same place

jdjejejeeeeeeeeeeeStep-by-step explanation:

Answer:

Please read the complete procedure below:

Step-by-step explanation:

You have the following initial value problem:

[tex]y'+2y=4t\\\\y(0)=8[/tex]

a) The algebraic equation obtain by using the Laplace transform is:

[tex]L[y']+2L[y]=4L[t]\\\\L[y']=sY(s)-y(0)\ \ \ \ (1)\\\\L[t]=\frac{1}{s^2}\ \ \ \ \ (2)\\\\[/tex]

next, you replace (1) and (2):

[tex]sY(s)-y(0)+2Y(s)=\frac{4}{s^2}\\\\sY(s)+2Y(s)-8=\frac{4}{s^2}[/tex]  (this is the algebraic equation)

b)

[tex]sY(s)+2Y(s)-8=\frac{4}{s^2}\\\\Y(s)[s+2]=\frac{4}{s^2}+8\\\\Y(s)=\frac{4+8s^2}{s^2(s+2)}[/tex] (this is the solution for Y(s))

c)

[tex]y(t)=L^{-1}Y(s)=L^{-1}[\frac{4}{s^2(s+2)}+\frac{8}{s+2}]\\\\=L^{-1}[\frac{4}{s^2(s+2)}]+L^{-1}[\frac{8}{s+2}]\\\\=L^{-1}[\frac{4}{s^2(s+2)}]+8e^{-2t}[/tex]

To find the inverse Laplace transform of the first term you use partial fractions:

[tex]\frac{4}{s^2(s+2)}=\frac{-s+2}{s^2}+\frac{1}{s+2}\\\\=(\frac{-1}{s}+\frac{2}{s^2})+\frac{1}{s+2}[/tex]

Thus, you have:

[tex]y(t)=L^{-1}[\frac{4}{s^2(s+2)}]+8e^{-2t}\\\\y(t)=L^{-1}[\frac{-1}{s}+\frac{2}{s^2}]+L^{-1}[\frac{1}{s+2}]+8e^{-2t}\\\\y(t)=-1+2t+e^{-2t}+8e^{-2t}=-1+2t+9e^{-2t}[/tex]  

(this is the solution to the differential equation)

Answer:

I THINK ITS B

Step-by-step explanation:

Answer:

[tex]f(x) -g(x) =(5x^3) +(-4x^2- 3x^2) + (0+2x) +(10-7)[/tex]

And if we simplify we got:

[tex]f(x) -g(x) =5x^3 -7x^2 +2x+ 3[/tex]

And the best option for this case is:

A) 5x3-7x2+2x+3

Step-by-step explanation:

For this case we have this function given:

[tex] f(x) = 5x^3 -4x^2 +10[/tex]

And we want to subracr from the last function this one:

[tex] g(x) =3x^2 -2x+7[/tex]

So we want to find [tex] f(x)-g(x)[/tex] and replacing we got:

[tex]f(x) -g(x) =(5x^3 -4x^2 +10) -(3x^2 -2x +7)[/tex]

And if we aggrupate the terms we got:

[tex]f(x) -g(x) =(5x^3) +(-4x^2- 3x^2) + (0+2x) +(10-7)[/tex]

And if we simplify we got:

[tex]f(x) -g(x) =5x^3 -7x^2 +2x+ 3[/tex]

And the best option for this case is:

A) 5x3-7x2+2x+3

Answer: the slope is -3

Step-by-step explanation:

(Pls see pic for the work)