Pls help

Consider functions fand g below.

g(x)=-x^2+2x+4


A.As x approaches infinity, the value of f(x) increases and the value of g(x) decreases.

B.As x approaches infinity, the values of f(x) and g(x) both decrease.

C.As x approaches infinity, the values of f(x) and g(x) both increase.

D.As x approaches infinity, the value of f(x) decreases and the value of g(x) increases.

Answer:

16

Step-by-step explanation:

Set up the equation ->

x+32=3x  

(you can get this easily by writing the equation down as you read the problem)

--> revisiting  x+32=3x

-x on both sides to isolate the number and put the like terms together

We are left with  32=2x

Divide 2 on both sides, and you will get x (his current age) --> x=16

Roger is currently 16 years old.

Answer:

16

Step-by-step explanation:

3x = 32 + x

2x = 32

x = 16

Answer:

1) Slope of the line  \(y = \frac{-3}{2}\)

2)Slope of the line m = 2

3) slope of the line m = -5

Step-by-step explanation:

Step(i):-

Given that equation of the straight line 3 x+2 y =0

The slope - intercept form    y = mx +c

                                              2 y = - 3x

                                              \(y = \frac{-3}{2} x\)

Slope of the line  \(y = \frac{-3}{2}\)

Step(ii):-

Given that equation of the straight line 2 x- y = 3

The slope - intercept form    y = mx +c

                                              y = 2x -3

slope of the line m = 2

Step(iii):-

Given that equation of the straight line 5 x + y = 10

The slope - intercept form    y = mx +c

                                              y = -5x +10

slope of the line m = -5

Therefore, the option that uses more than 1/4 of a foot of ribbon to create a single bow will result in the longest ribbon.

Finding the value of just one unit and using that value to determine the value of any multiples of that unit is known as the unitary approach. Direct or inverse relationship between two factors is involved. It is frequently used to determine the cost of a single object when the cost for a particular number of items is known, as well as other ratio and proportion-related problems.

given

Each bow needs 1/4 of a foot of ribbon if Mary uses 1/2 of a foot to create two bows (since 1/2 2 = 1/4).

which option creates the longest ribbon. Assume Tonya needs x feet of fabric to create just one bow.

Mary uses 1/4 of a foot of ribbon to create one bow, so we can establish the disparity shown below:

x > 1/4

This is due to the fact that Tonya must use more ribbon than Mary does—more than 1/4 of a foot—to create a single bow.

Therefore, the option that uses more than 1/4 of a foot of ribbon to create a single bow will result in the longest ribbon.

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Answer:

11 buses

Step-by-step explanation:

Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005

Answer:

−2(3c  +  7)

Step-by-step explanation:

Factor the polyomial

The interval of the domain of the considered function for which the function is decreasing is none. The function is strictly increasing: Option D: The function is increasing only.

Suppose that the function is y = f(x)

If for an interval I, when x increases meanwhile staying in the interval I, the function's output decreases (or can stay same), then we say that the function is decreasing in the interval I.

This interval I was of values that x can take for this function, which is the domain of the considered function, so we say:

y = f(x) is decreasing function in an interval I if:

\(f(x+\delta) \leq f(x) \: \forall x \in I : x+\delta \in I\)

If we have:

\(f(x+\delta) < f(x) \: \forall x \in I : x+\delta \in I\), then the function is called strictly decreasing in the interval I.

Similarly, there increasing( \(f(x+\delta) \geq f(x) \: \forall x \in I : x+\delta \in I\) ) and strictly increasing(\(f(x+\delta) > f(x) \: \forall x \in I : x+\delta \in I\) ) functions.

For this case, the function is:

\(h(x) = \left \{ {{2^x, x < 1} \atop \: \atop {\sqrt{x+3}, x \geq 1}} \right.\)

The function is differentiable in either side of 1.

Sign of rate of function at a point tells whether its increasing or decreasing.

\(h'(x)= 2^x ln(2)\)
We know that:

\(2^x > 0 \: \rm \forlall x \in \mathbb R\)

And \(ln(2) \approx 0.69 > 0\)

Thus, \(h'(x)= 2^x ln(2) > 0 \: \forall x \in \mathbb R\)

So, rate is positive, the function is strictly increasing for this case.

\(h'(x) = \dfrac{1}{2\sqrt{(x+3)}}\)

For all x > 1, \(\sqrt{x+3} > 0\), and so as h'(x)

So rate is positive and therefore strictly increasing for this case too.

\(h(1+\delta) - h(1)= \sqrt{1+\delta + 3} - \sqrt{1+3} = \sqrt{4+\delta} - \sqrt{4} > 0 \forall \delta > 0\)

So rate of the considered function is positive,so function is strictly increasing all over the domain.

Thus, the interval of the domain of the considered function for which the function is decreasing is none. The function is strictly increasing: Option D: The function is increasing only.

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The number of years it would take is approximately equal to 53 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

By substituting given parameters, we have the following:

96627 = 11211(1 + 0.0418)^t

8.61894567835 = (1.0418)^t

By taking the ln of both sides, we have:

Time, t = ln(8.61894567835)/ln(1.0418)

Time, t = 52.60 ≈ 53 years.

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Answer:

The number of commercial orbital launches is equal to 19 and the number of noncommercial orbital launches is equal to 40.

Step-by-step explanation:

IMPORTANT INFORMATION: The number of noncommercial orbital launches was two more than twice the number of commercial orbital launches.

Let's say that the number of commercial orbital launches is equal to x. Now, the number of noncommercial orbital launches is equal to 2x+2.

We are told that if we add the number of commercial and noncommercial orbital launches together we will get 59.

Therefore, if we add 2x+2 with x we should get 59:

2x+2+x=59

3x+2=59

3x=57

x=19

This is how we can come to the answer that the number of commercial orbital launches is equal to 19 and the number of noncommercial orbital launches is equal to 40 (2x+2=2*19+2=38+2=40).

Hope this helps!

Answer:

As shown in picture, if MC is median of triangle ABC, M is midpoint of AB.

Denote the coordinate of A, B and M are (Ax, Ay), (Bx, By) and (Mx, My) respectively.

The formula relating coordinate of A, B and M is:

Ax + Bx = 2Mx

Ay + By = 2My

In detail,

-1 + Bx = 2 x 4 => -1 + Bx = 8 => Bx = 9

11 + By = 2 x 11 = > 11 + By = 22 => By = 11

=> Option D is correct

Hope this helps!

:)

Answer:

595.

Step-by-step explanation:

Take $2000 and subtract $810 from it. You now have the total of the two pieces of equipment without the extra pricing. You should get $1,190. Then divide that number by 2. You will get $595.

1st Piece of Equipment = $595

2nd Piece of Equipment = $1,405

2nd Piece is $810 more expensive and the two pieces combined is $2,000.

The laptop computer will be worth $700 or less after 6 years.

To determine the number of years it takes for the laptop computer to be worth $700 or less, we can set up an equation based on the given information.

Let's denote the initial value of the laptop as V0 = $2900. Each subsequent year, its value will be 70% of its value the previous year.

So, the value of the laptop after one year would be V1 = 0.7 * V0 = 0.7 * $2900 = $2030.

In general, the value of the laptop after n years can be represented as Vn = \(0.7^n\) * V0.

We want to find the value of n when Vn ≤ $700. Thus, we can set up the following inequality:

\(0.7^n\) * V0 ≤ $700

Substituting the value of V0, we get:

\(0.7^n\) * $2900 ≤ $700

Dividing both sides of the inequality by $2900, we have:

\(0.7^n\) ≤ $700 / $2900

\(0.7^n\) ≤ 0.2414

To solve for n, we can take the logarithm (base 0.7) of both sides:

n ≤ log0.7(0.2414)

Using logarithmic properties, we can rewrite this as:

n ≤ log(0.2414) / log(0.7)

Using a calculator, we find:

n ≤ 6.54 (rounded to two decimal places)

Since n represents the number of years, it must be a whole number.

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Step-by-step explanation:

step 1. A = P(1 + r/n)^nt. this is the compounding equation where n is the number of compounds, t is the time in years, and r is the rate.

step 2. A = 685(1 + .051/1)^(1(1/4))

step 3. A = 693.57.

Radius of the can is 3.71 cm.

What is Volume of cylinder?

Volume of cylinder is calculated as;

V =  π r² h

Given that;

Volume of a cylindrical can = 550 cm³

Height of the can = 12 cm

Since, Volume of a cylinder = π r² h

After substitute all values we get;

V = π r² h

r² = V / π h

r² = 550/3.14*12

r² = 550/37.68

r² = 13.8

r = √13.8

r = 3.71 cm

Hence, Radius of the can is 3.71 cm.

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a)The value of acceleration will be 4.8 m/s²

b)The total distance travelled is 505 m.

a) As all the movement happens along a straight line, we need to define an axis only, which we call x-axis, being the positive direction the one followed by the car.

We can choose to place our origin at the location where the motorcycle was stopped at the side of the road (assuming that it is the same point  for the car when it passes him), so our initial position is 0.

We can also choose our time origin to be the same as the instant that the motorcycle starts from rest, so t₀ = 0.

With these assumptions, and assuming also that the acceleration is constant, we can write two equations, one for the car (at constant speed) and the another one for the motorcycle, as follows:

xc = vx*t

xm= 1/2*a*t²

When the motorcycle passes the car, both distances traveled from the origin will be equal each other, i.e., xc = xm :

⇒ vx*t = 1/2*a*t²

We have as givens vx=35 m/s and t = 14.5 sec when both equations are equal each other.

⇒ 35 m/s* 14.5 s = 1/2*a*(14.5)²(s)²

Solving for a:

a = (2* 35 m/s) / 14.5 s = 4.8 m/s²

b) Replacing the value of a in the equation for xm, we have:

xm = 1/2*4.8 m/s²* (14.5)²s² = 505 m.

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Answer:

\(C = 25.1 \text{ cm}\)

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

\(C = \pi d\)

Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).

↓ plugging in the given radius

\(C = 8\pi \text{ cm}\)

↓ rounding to the nearest tenth

\(\boxed{C = 25.1 \text{ cm}}\)

Answer:

12+8x=84

Step-by-step explanation:

her flat fee is $12

$8 for any extra child

84 is the total she received which is the sum of 12 + 8×the extra number of children

The number of degrees below zero is given by A = 56° F

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the initial temperature be represented as T

Let the number of degrees below zero be A

Now , the value of T is

T = -56° F

From the modulus function , we get

The value of the modulus function is always non-negative.

So , the measure of A = | T |

A = | -56 |

A = 56° F

Hence , the number of degrees below zero is 56° F

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Answer:

(4, 0)

Step-by-step explanation:

A is 3 units to the left of x = 1, so A' will be 3 units to the right of x = 1.

This means A' has coordinates (4, 0).

The number of square feet needed to cover the hole is 44ft²

To find this, we need to find the area of the green region and subtract the little square that it has inside.

Remember that for a rectangle, the area is the product between the dimensions, then the area of the green region is:

A = 12ft*4ft = 48ft²

The little square has an area:

a = 2ft*2ft = 4ft²

Then the area needed is:

area = 48ft² - 4ft² = 44ft²

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It shows that lim(6n⁴ + (-1)ⁿ2n³ + 5) = 2 by the ε - K definition of the limit of a sequence.

To show that lim(6n⁴ + (-1)ⁿ2n³ + 5) = 2, we need to show that for any ε > 0, there exists a positive integer K such that for all n ≥ K, |(6n⁴ + (-1)ⁿ2n³ + 5) - 2| < ε.

Let ε > 0 be arbitrary. We need to find a K such that for all n ≥ K, |(6n⁴ + (-1)ⁿ2n³ + 5) - 2| < ε.

Note that |6n⁴ + (-1)ⁿ2n³ + 5 - 2| = |6n⁴ + (-1)ⁿ2n³ + 3|.

For n = 1, 2, 3, ... we have:

|6n⁴ + (-1)ⁿ2n³ + 3| = 6n⁴ + 2n³ + 3 when n is even

|6n⁴ + (-1)ⁿ2n³ + 3| = 6n⁴ - 2n³ + 3 when n is odd

Thus, for any n, we have:

|6n⁴ + (-1)ⁿ2n³ + 3| ≤ 6n⁴ + 2n³ + 3

We want to find a K such that for all n ≥ K, |6n⁴ + (-1)ⁿ2n³ + 3| < ε + 1.

We can start by setting ε + 1 = 6K⁴ + 2K³ + 3, and solving for K.

ε + 1 = 6K⁴ + 2K³ + 3

ε = 6K⁴ + 2K³ - 2

Since the terms with the highest power of K grow the fastest, we can ignore the 2K³ term and find K such that 6K⁴ < ε/2. Thus, we have:

6K⁴ < ε/2

K⁴ < ε/12

K < (ε/12)^(1/4)

Let K be the smallest integer greater than (ε/12)^(1/4). Then for all n ≥ K, we have:

|6n⁴ + (-1)ⁿ2n³ + 3| ≤ 6n⁴ + 2n³ + 3

< 6n⁴ + 2n⁴ + 3 (for n ≥ K, n⁴ > K⁴ > ε/12)

= 8n⁴ + 3

Let N be any integer greater than or equal to K. Then for any n ≥ N, we have:

|6n⁴ + (-1)ⁿ2n³ + 5 - 2| = |6n⁴ + (-1)ⁿ2n³ + 3| < 8n⁴ + 3

< 8N⁴ + 3 (since n ≥ N)

< 8K⁴ + 3 (since N ≥ K)

< ε/2 + 3 (since K was chosen such that 6K⁴ < ε/2)

< ε

This shows that lim(6n⁴ + (-1)ⁿ2n³ + 5) = 2 by the ε - K definition of the limit of a sequence.

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Answer:

Step-by-step explanation:

-2b(exponent 6)c(exponent 2)

The function f ( x ) = y = 2 ( x + 5 )² - 6 is a one to one function

What is one to one function?

One to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets. It is also written as 1-1. In terms of function, it is stated as if f(x) = f(y) implies x = y, then function f is one to one.

The function, f(x), is a one to one function when one unique element from its domain will return each element of its range. This means that for every value of x, there will be a unique value of y or f(x).

f ( x₁ ) = f ( x₂ ) if and only if x₁ = x₂

Given data ,

Let the function be f ( x )

where f ( x ) = y

So , the equation will be

y =  2 ( x + 5 )² - 6

Now , on simplifying the equation , we get

y = 2 ( x² + 10x + 25 ) - 6

y = 2x² + 20x + 50 - 6

y = 2x² + 20x + 44

Therefore , the function is f ( x ) = y = 2x² + 20x + 44

Now , replace y with x , we get

f ( y ) = x = 2y² + 20 y + 44

And f ( x₁ ) = f ( x₂ )

So , the function is one to one function

Hence , The function f ( x ) = y = 2 ( x + 5 )² - 6 is a one to one function

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Answer:

D) 312 cubic yards

Step-by-step explanation:

large box = 9x8x4=288

small box = 2x3x4=24

288+24=312

Answer:

20/21

Step-by-step explanation:

The solution of the equation -x² + 4 = x + 2 is at x = -2 and x = 1

An equation is an expression that shows how numbers and variables are related to each other.

Given the quadratic equation:

-x² + 4 = x + 2

Collecting like terms:

x² + x - 2 = 0

Plotting using a graph; the solution of the equation can be gotten by getting the point the graph crosses the x axis.

The solution is at x = -2 and x = 1

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The temperature drops by \(31\°C\) from day to night in this city.

To calculate the temperature drop from day to night in \(\°C\), we subtract the average nightly low temperature from the average daily high temperature.

Given:

Average nightly low temperature: \(-40\°C\)

Average daily high temperature: \(-9\°C\)

The temperature drop can be calculated as:

Temperature drop = Average daily high temperature - Average nightly low temperature

Substituting the given values:

Temperature drop = \(-9\°C - (-40\°C)\)

Simplifying the equation:

Temperature drop = \(-9\°C + 40\°C\)

Temperature drop = \(31\°C\)

The concept of temperature drop refers to the difference in temperature between two specific periods or conditions. In this case, we are looking at the temperature drop from day to night in a city in China known for its cold climate.

Therefore, the temperature drops by \(31\°C\) from day to night in this city.

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