Evaluate the following functions for the given value.
20. g(x) = x-3/2x+1 ; -1

Answer:

Distance = 15

Step-by-step explanation:

4 - (-11) = 4 + 11 = 15

Based on the given summation notation, the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n

The expression is given as:

43Σn=1(3+9n)

As a general rule, if a summation notation is represented using the following expression

Σ(a + bn)

The equivalent expression of the above summation notation is

Σa + bn

Where the variable a is a constant in the expression

This means that:

Σ(a + bn) = Σa + bn

Using the above equation as a guide, we have the following equivalent equation

43 Σ n=1 (3+9n) = 43 Σ n=1 3 + 43 Σ n=1 9n

Hence, based on the given summation notation; the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n

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Answer:

D on 3dg I took the best

Step-by-step explanation:

By the fundamental theorem of calculus,

[tex]\displaystyle y = \int_0^v \sqrt{3+4t^2} \, dt \implies \boxed{\frac{dy}{dv} = \sqrt{3+4v^2}}[/tex]

In general,

[tex]\displaystyle \frac{d}{dx} \int_0^{g(x)} f(u) \, du = f(g(x)) \frac{dg}{dx}[/tex]

The true statement is (c) the function f(x) is an exponential function

From the table, we can see that:

This means that the table represents an exponential function

The rate is then calculated as:

f(n) = f(1) * r^n-1

Using f(3), we have

102 = 17 * r^3-1

This gives

r^2 = 6

Take the square roots

r = 2.45

Hence, the true statement is (c) the function f(x) is an exponential function

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Answer:

[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]

Step-by-step explanation:

Given quadratic function:

[tex]f(x)=2x^2-x-10[/tex]

The x-intercepts of the graph are the points at which the curve crosses the x-axis, so when f(x) = 0.

To find these points, factor the quadratic equation, set it to zero, then solve for x.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.

[tex]\implies ac=2 \cdot -10 = -20[/tex]

[tex]\implies b=-1[/tex]

Therefore, the two numbers are -5 and 4.

Rewrite the middle term as the sum of these two numbers:

[tex]\implies 2x^2-5x+4x-10[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(2x-5)+2(2x-5)[/tex]

Factor out the common term (2x - 5):

[tex]\implies (x+2)(2x-5)[/tex]

Set the factored function to zero:

[tex]\implies (x+2)(2x-5)=0[/tex]

Apply the zero-product property:

[tex]\implies (x+2)=0 \implies x=-2[/tex]

[tex]\implies (2x-5)=0 \implies x=\dfrac{5}{2}[/tex]

Therefore, the x-intercepts of the graph are:

[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]

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The correct answer for the solution of  inequality  is [tex]x\geq 8[/tex].

Let the unknown number be "[tex]x[/tex]."

The statement  "a number plus four" can be written  as "[tex]x+4[/tex]."

The phrase "is greater than or equal to twelve" can be expressed as "[tex]\geq 12.[/tex]

Put these together, the inequality becomes:

[tex]x + 4\geq 12[/tex]

solve for "[tex]x[/tex],"  isolate the variable on one side of the inequality:

Subtract -[tex]4[/tex] from both side of the expression:

[tex]x + 4 - 4 \geq 12 - 4[/tex]

[tex]x\geq 8[/tex]

The correct expression for the  inequality is  [tex]x\geq 8[/tex]

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Answer:

ight first you add 4 to 6 and that gets you 10 so you left with p+5=10 then you subtract 5 from 10 so p is gonna be  5

Step-by-step explanation:

Answer:

[tex] - 3 \times - 1 = 3 \\ \\ 5 - 2 = 3[/tex]

Step-by-step explanation:

3,3

Answer: Second Choice. (3, 3)

Step-by-step explanation:

Given point

(x, y) = (-3, 5)

Given the rule for application

(-x, y - 2)

Determine the new x-value

x = -3

-x = - (-3) = 3

Determine the new y-value

y = 5

y - 2 = (5) - 2 = 3

Therefore, the result is [tex]\Large\boxed{(3,~3)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The slope of the points on the graph is 4/3

The points on the graph are

(x, y) = (4,3) and (1, -1)

Slope is calculated as:

m = (y2 - y1)/(x2 - x1)

This gives

m = (-1 - 3)/(1 - 4)

Evaluate

m = 4/3

Hence, the slope of the points on the graph is 4/3

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The area of the garden is 74 square feet

The complete question is added as an attachment

From the attached figure, we have the following shapes and dimensions:

The rectangular area is

A1 = 10 * 5

Evaluate

A1 = 50

The area of the trapezoid is

A2 = 0.5 * Sum of parallel bases * height

This gives

A2 = 0.5 * (10 + 6) * 3

Evaluate

A2 = 24

The total area is

Total = A1 + A2

This gives

Total = 50 + 24

Evaluate

Total = 74

Hence, the area of the garden is 74 square feet

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The rat population is 2004 and 2012 are 24. 8 millions and 31. 6 millions respectively.

Given the function of the population to be;

n (t) = 24 e^0. 015t

Where;

In 2004, t = 1

Substitute into the formula;

n(1) = 24 e^0. 015t

n(1) = 24 e^(0.015 × 1)

n(1) = 24 e^0. 015

n(1) = 24. 8 millions

In year 2012, t = 8

n(8) = 24 e^(0. 015 × 8)

n(8) = 24e^0. 12

n(8) = 31. 6 millions

Thus, the rat population is 2004 and 2012 are 24. 8 millions and 31. 6 millions respectively.

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Answer: 8 x 10^2

Step-by-step explanation:

scientific notation has to be greater than 1, less than 10

therefore:

0.08 = 8 x 10^2

Using it's concept, the probabilities are given as follows:

a) C. 7/20.

b) D. 15/22.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For item a, we have that there are 60 students with no curfew, and of those, 21 have no chores, hence the probability is given by:

p = 21/60 = 7/20

Which means that option C is correct.

For item b, we have that there are 66 students with no shores, and of those, 45 have a curfew, hence the probability is given by:

p = 45/66 = 15/22

Which means that option D is correct.

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Answer:

See below

Step-by-step explanation:

The derivative of the function is the slope

2x^2 - x -1       take derivative  ( f ' )

4x -1                 equate to 7

7 = 4x -1

x = 2        sub into the original equation to find y = 5

Answer:

[tex]x^2+y^2=64[/tex]

Step-by-step explanation:

So the first important thing in solving this problem, is identifying what the major and minor axis are. The major axis is the bigger one, and we want to find on which axis it is.

So by simply looking at the eclipse, you can see that it's larger on the horizontal axis, so the major axis is on the horizontal axis, and the minor axis is on the vertical axis.

This means the equation will be expressed as:

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1[/tex]

In this equation the major axis, has a length of 2a, and the minor axis has a length of 2b. It's also important to note that (h, k) is the middle of the eclipse, but in the equation you provided, there is no subtraction, so it's just 0, meaning the center is at the origin (0, 0)

So now let's solve for a, and b. I'll look at each individual fraction separately.

[tex]\frac{x^2}{64}[/tex]

The denominator is equal to the value of a^2, so we simply take the square root of this to get the equation: a=8

[tex]\frac{y^2}{36}[/tex]

The denominator is equal to the value of b^2, so we simply take the square root of this to get the equation: b=6

So by just looking at the graph the larger circle appears to have a denominator that is equal to the length of the major axis. The major axis is equal to 2a, and since we know the value of a (8), we simply multiply this by 2 to get a length of 16. This was a bit redundant to do, since in the equation of a circle we need the radius, and the radius is just half the diameter, so now we divide this 16 by 2 to get a radius of 8.

The circle also appears to be centered at the origin so the equation will have (x-0)^2 and (y-0)^2 which is just x^2 and y^2

Plugging in all the values we get the equation:

[tex]x^2+y^2=64[/tex]

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

The ellipse shown here is a horizontal ellipse that has major axis parallel to x - axis and minor axis parallel to y - axis. Length of major axis = 2a, and that of minor axis = 2b.

And it has it's centre on origin, it's equation can be written as :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

so, let's equate given equation with the standard equation ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{64} + \cfrac{ {y}^{2} }{36} = 1[/tex]

so we get :

As we know, length of major axis is : 2a = 2 × 8 = 16 units

and, the larger circle has diameter = 2a = 16 units

so, it's radius = 8 units ~

Now, let's write the equation of circle with origin as centre and radius = 8 units

[tex]\qquad \sf  \dashrightarrow \: {(x - h)}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]

[ h = 0, k = 0, since circle has centre at origin ]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + {y}^{2} = 64[/tex]

Answer:

x = 8 ± [tex]\sqrt{10}[/tex]

Step-by-step explanation:

x² - 16x + 54 = 0 ( subtract 54 from both sides )

x² - 16x = - 54

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 54 + 64

(x - 8)² = 10 ( take the square root of both sides )

x - 8 = ± [tex]\sqrt{10}[/tex] ( add 8 to both sides )

x = 8 ± [tex]\sqrt{10}[/tex]

then

x = 8 - [tex]\sqrt{10}[/tex] , x = 8 + [tex]\sqrt{10}[/tex]

In the process of solving the expression x − 5 =radical 3x −11 , you will need to solve the quadratic equation x² - 13x + 36 =0

Radical equations are expression that are under the square root. For instance √x is a radical expression.

Given the equation expressed as:

x − 5 = √3x −11

Square both sides to have;

(x-5)² = (√3x −11 )²

This can be further expressed as:

(x-5)² =3x −11

Expand

x² -10x + 25 = 3x - 11

Equate to zero

x² -10x + 25 - 3x +11 = 0
x² -10x - 3x +36 = 0
x² - 13x + 36 =0

Hence in the process of solving the expression x − 5 =radical 3x −11 , you will need to solve the quadratic equation x² - 13x + 36 =0

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There are 120 ways to color the 4 rectangles

The given parameters are:

Paints, n = 5

Rectangles, = 4

The number of ways to color the rectangles is

[tex]Ways = ^nP_r[/tex]

This gives

[tex]Ways = ^5P_4[/tex]

Apply the permutation formula

[tex]Ways = \frac{5!}{1!}[/tex]

Evaluate the expression

Ways = 120

Hence, there are 120 ways to color the 4 rectangles

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Answer:

[tex]\dfrac{8}{\sin(6^\circ)} \approx 76.53[/tex]

Step-by-step explanation:

[tex]UX \sin(6^\circ) = 8 \Rightarrow \boxed{UX = \dfrac{8}{\sin(6^\circ)} \approx 76.53}[/tex]

Sis : you : bro

10 : 9 : ?

? ? : 27 : 29

We can get the 9 at the top to 27, by multiplying the whole row by 3 to get:

30 : 27 :?

? : 27 : 29

Your age matches (in the ratios or relation to your sis & bro) now 27 yrs in both ratio. Creating a single ratio, whereby multiplying the top row by 3 to get you to 27 & bottom row by 1 to get you to 27. Knowing when you're 27 in both cases, you know how old your sis & bro is

So, replace the ? with the number above or below it, creating a single ratio, where you are in common with both, by being 27 in both cases.

The ratio of sis : you : bro is now -

The ratio of sis : you : bro is now - 30: 27 : 29

To find what your age is we need to increase the ratio in the same amount to find your maximum age under 70.

So, if we were to double your age to 54, by multiplying your previous age of 27 by 2. We've got to do the same for your sis & bro too, they're aging with you.

We get :

We get :60 : 54 : 58

(30 x 2) : (27 x2) : (29 x2)

Keep increasing the ratio, to the point you're not above 70 years. Now, I'll multiply all ages by 3.

30: 27 : 29

(30 x 3) : ( 27 x 3) : (29 x 3)

We get:

We get:90 : 81 : 87

Right now, you're above the age of 70.

Thus, your maximum age must be 54, where you're under 70 years, but over 40 years.

Answer : 54 years

Hope this helps!

The standard form the weight of a pitaya seed is 1 x 10⁷ ounces.

Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is referred to as being in standard form. If you look closely, you will see that 1.23 is a decimal between 1.0 and 10.0, and as a result, we have the standard form of 123,000,000 as 1.23 x 10⁸.

Given that a pitaya, or dragon fruit, is a tropical fruit with pink skin and pulp filled with tiny black seeds. The weight of a pitaya seed is 1 x 10⁷ ounces.

The standard form can be written as:-

Weight = 10000000 ounces

Weight = 1 x 10⁷   ounces.

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The events E1 and E2 are not independent events.

The two events are given as:

E1 and E2 such that

P(E1) = 0.27, P(E2) = 0.40 and P(E1 U E2) = 0.58.

The two events E1 and E2 are independent if the following equation is true

P(E1 and E2) = P(E1) * P(E2)

Where

P(E1 and E2) = P(E1) + P(E2) - P(E1 U E2)

Substitute the known values in the above equation

P(E1 and E2) = 0.27 + 0.40 - 0.58

Evaluate the sum in the above equation

P(E1 and E2) = 0.67 - 0.58

Evaluate the difference in the above equation

P(E1 and E2) = 0.09

Substitute P(E1 and E2) = 0.09 in P(E1 and E2) = P(E1) * P(E2)

P(E1) * P(E2) = 0.09

Substitute P(E1) = 0.27 and P(E2) = 0.40 in the above equation

0.27 * 0.40 = 0.09

Evaluate the product

0.108 = 0.09

The above is false because 0.108 and 0.09 are not equal

Hence, the events E1 and E2 are not independent events.

How to solve for x

We  have:

P(A) = x

P(B) = x + 0.2

P(A n B) = 0.15

For independent events, we have:

P(A) * P(B) = P(A n B)

So, we have:

x * (x + 0.2) = 0.15

Expand

x^2 + 0.2x - 0.15 = 0

Using  a graphing calculator, we have:

x = 0.3

Hence, the value of x is 0.3

The value of P(A U B)

This is calculated using

P(A U B) = P(A) + P(B) - P(A n B)

Substitute the known values in the above equation

P(A U B) = x + x + 0.2 - 0.15

Evaluate the like terms

P(A U B) = 2x + 0.05

Substitute 0.3 for x

P(A U B) = 2 * 0.3 + 0.05

Evaluate

P(A U B) = 0.65

Hence, the value of P(A U B) is 0.65

The value of P(A' U B')

This is calculated using

P(A' U B') = P(A') + P(B') - P(A' n B')

Where

P(A') = 1 - x

P(B') = 1 - x - 0.2 = 0.8 - x

P(A' n B') = P(A') * P(B')

P(A' n B') = (1 - x) * (0.8 - x)

Substitute the known values in the equation P(A' U B') = P(A') + P(B') - P(A' n B')

P(A' U B') = (1 - x) + (0.8 - x) - (1 - x) * (0.8 - x)

Substitute 0.3 for x

P(A' U B') = (1 - 0.3) + (0.8 - 0.3) - (1 - 0.3) * (0.8 - 0.3)

Evaluate

P(A' U B') = 0.85

Hence, the value of P(A' U B') is 0.85

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The variable overhead rate variance is: c. $6,052 U.

First step is to calculate variable component of the predetermined overhead rate using this formula

Variable component of the predetermined overhead rate= Budgeted variable manufacturing overhead/Budgeted hours

Let plug in the formula

Variable component of the predetermined overhead rate=$ 28,200/12,000 labor-hours

Variable component of the predetermined overhead rate=$2.35 per labor-hour

Second step is to calculate  variable overhead rate variance using this formula

Variable overhead rate variance=(AH×AR)-(AH×SR)

Let plug in the formula

Variable overhead rate variance= $ 26,967- ( 8,900 labor-hours×$2.35 per labor-hour)

Variable overhead rate variance= $ 26,967- $20,915

Variable overhead rate variance= $6,052 U (Unfavorable)

Therefore the variable overhead rate variance is: c. $6,052 U.

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The limit is

[tex]\displaystyle \lim_{x\to\infty} \frac{3x^{7/2} + 7x^{-1/2}}{x^2 - x^{1/2}} = \lim_{x\to\infty} \frac{3x^{3/2} + 7x^{-5/2}}{1 - x^{-3/2}} = \boxed{\infty}[/tex]

since the degree of the numerator exceeds the degree of the denominator.

Hello and Good Morning/Afternoon!

Let's take this problem step by step:

Let's consider some facts:

 ⇒ angles are opposite each other

    ⇒ by the Vertical Angle Theorem

        ⇒ angles opposite each other are equal in measure

So:

 [tex]\hookrightarrow 4x + 12 = 64[/tex]

Let's solve

  [tex]4x + 12 = 64\\4x = 52\\x = 13[/tex]

x's value is 13

Answer: 13

Hope that helps!

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The equation for the trajectories orthogonal to the family of functions of the form 5 · x² - 2 · y² = C is equal to (1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C.

In this problem we have a family of functions in implicit form, that is, a function of the form f(x, y, c) = 0. The equation of a orthogonal trajectory is always perpendicular to a particular form of a equation. First, we determine the first derivative of the given expression:

5 · x² - 2 · y² = C

10 · x - 4 · y · y' = 0

4 · y · y' = 10 · x

y' = (10 · x) / (4 · y)

y' = (5 · x) / (2 · y)

If f(x, y) = (5 · x) / (2 · y), then the differential equation for the orthogonal trajectories related to the family of functions is:

y' = - 1 / f(x, y)

y' = - (2 · y) / (5 · x)

dy / (2 · y) = - dx / (5 · x)

By indefinite integration we get the following solution to the ordinary differential equation:

(1 / 2) · ㏑ y = - (1 / 5) · ㏑ x + C

(1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C

The equation for the trajectories orthogonal to the family of functions of the form 5 · x² - 2 · y² = C is equal to (1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C.

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He will be left no money after buying 25 copies because he has 1900 rupees less.

Given that Usman buys 8 books that cost Rs. 120/ each, he will be left Rs. 140.

The cost of 1 books is Rs 120.

The cost of 8 book is 120×8=960.

The cost of 25 books is 120×25=3000

To find the money usman will left with him is the difference between the total money and the cost of 25 books.

Total money=960+140=1100

money left=Total money -cost of 25 books

money left=1100-3000

Usman have less money to buy 25 books. He has 1900 rupees less to buy 25 books.

Hence, Usman does leave any money with even he has less money to buy 25 books

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Answer:

Step-by-step explanation:

The radius of the base is the distance between the center of the circle and the edge of the base, therefore in this case it is equal to 3 in.

The volume of a cone is given by:

V = π * r² * h / 3

V = π * (3)² * 10 / 3

V = 94. 25 in³

Therefore, The volume of is 94. 25 in³.

Step-by-step explanation:

6.25 points

Find the GCF for the list.

10m4, 40m⁹

10m5

40m4

10m4

6.25 points

list