Evaluate the following given f(x)=4x+3 and g(x)=x^2+4x-1. Determine the domain of each.

1. f(4)

2. g(2)

3. f(x+3)

4. g(x+2)

Answer:

(0.5,1)

Step-by-step explanation:

The midpoint formula is \((\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)

Let's do x first

-1+2=1

1 ÷2=0.5

y

5+-3=2

2÷2=1

(0.5,1)

Hope this helps :-)

Answer:

Anna had $125 in her account before the deposit. Here's the math:

$150 (current balance) - $25 (deposit) = $125 (previous balance)

h: The domain

-5 ≤ x ≤ 5

The amount of packaging used for each roll of haw flakes will decrease by 5% each year.

An exponential function is modeled as follows:

y = a(b)^(x/n).

In which:

The function for this problem is defined as follows:

f(a) = 4(0.95)^a.

The parameter b assumes a value of 0.95 < 1, meaning that the function represents exponential decay, and the decay rate is given as follows:

1 - r = 0.95

r = 1 - 0.95

r = 0.05.

Meaning that the amount of packaging used for each roll of haw flakes will decrease by 5% each year.

More can be learned about exponential functions at https://brainly.com/question/30113628

#SPJ1

Answer:

Its d

Step-by-step explanation:

Answer:

Probably 5

Step-by-step explanation:

This is an extremely confusing question.  Whoever wrote it most likely had a typo.

The little box in the corner of the triangle means that is 90 degrees. if that is the case, this is a simple question:

Apply pythagorean theorem (a^2 + b^2 = c^2)

In this case:

3^2 + 4^2 = x^2

x^2 = 25

x=5.

HOWEVER: the two given angles are 60 degrees and 50 degrees.

Which does not work. It creates an impossible triangle.

Cultural sensitivity is crucial in elder care. Cultural beliefs impact elderly care. A foreign-raised nursing student desires to care for her mother and sisters until her mother's passing.

Consider cultural values: Students from certain backgrounds may see caring for their elderly parents as a moral duty. Respecting elder beliefs is critical in discussing care options. Have open, non-judgmental communication with the nursing student. Show empathy and listen to her perspective.

Educate the nursing student about caring for a loved one with medical and psychiatric problems. Explain physical, emotional, and financial consequences, including effects on relationships and responsibilities.

Learn more about  Role Strain from

https://brainly.com/question/14283116

#SPJ1

Answer:

Express the given function h as a composition of two functions f and g so that h (x )equals (f circle g )(x )commah(x)=(f g)(x), where one of the functions is 4 x minus 3.4x−3. h (x )equals (4 x minus 3 )Superscript 8h(x)=(4x−3)8 f (x )f(x)equals=4 x minus 3. See answer. zalinskyerin2976 is waiting for your help.

Step-by-step explanation:

this what f  ;|

Answer:

x1=-1 ,x2=1

Step-by-step explanation:

Y= x² + 1 is Quadratic Equation rest all equations are  linear .

What does a linear equation mean in mathematics?

A equation in algebra is one that only has a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept.

                                 The aforementioned is occasionally referred to as a "linear equation with two variables," with x and y serving as the variables. The term "linear equation" refers to equations with power 1 variables. ax+b = 0 is an example of a single variable having real values for the variables a, b, and x.

A. Y = x - 1    =  linear function.

B. Y= 4x        =  linear function

C. Y= y=3      =  linear function.

D. Y= x² + 1   = Quadratic Equation

E. X=7           =  linear function

Learn more about Linear equation

brainly.com/question/11897796

#SPJ1

Answer:

like 20 percent

Under the units-of-activity method, the depreciation expense per mile for Bus #3 is $0.4616.

The units-of-activity method is one of the depreciation methods in use.

Under the units-of-activity method, the depreciation expense per unit is determined by dividing the depreciable amount by the total units of activity.

The depreciation amount (the value of the asset subject to depreciation) is the net of the total cost less the salvage value.

Depreciable amount of Bus #3 = $57,700 ($66,500 - $8,800)

Expected total miles for Bus #3 = 125,000

Depreciation expense per mile for Bus #3 = $0.4616 ($57,700 ÷ 125,000)

Learn more about determining the depreciation expense per unit at https://brainly.com/question/22077069.

#SPJ1

Bus    Acquired    Cost    Salvage    Useful Life     Depreciation
                                          Value         in Years          Method

1          1/1/12      $99,100   $7,900           4             Straight-line

2         1/1/12      128,000     11,000          4             Declining- balance

3         1/1/13       66,350      8,800          5             Unit-of-activity

The system of the equations that has a solution of (-2, 0, 1) will be x + y + z = -1, x + y + 2z = 0, and x + 2y + 3z = 1.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The system of the equations that has a solution of (-2, 0, 1) will be

Let the number of variables be x, y, and z.

Then we have

Then the first equation will be

x + y + z = -1

Then the second equation will be

x + y + 2z = 0

Then the third equation will be

x + 2y + 3z = 1

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ1

Answer:

$180

Step-by-step explanation:

If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180

Answer:

Total number of ways in which first, second and third prizes will be awarded = 560

Step-by-step explanation:

As given,

There are 16 players participated in a tennis tournament.

and 3 players will be awarded for first, second, and third prize.

As we know,

ⁿCₓ = \(\frac{n!}{x! (n-x)!}\)

n = the number of items.

x = how many items are taken at a time.

As given, n = 16 , x = 3

⇒¹⁶C₃ = \(\frac{16!}{3! (16-3)!} = \frac{16!}{3! (13)!} = \frac{16.15.14.13!}{3! (13)!} = \frac{16.15.14}{3!} = \frac{16.15.14}{3.2.1} = \frac{3360}{6} = 560\)

∴ we get

Total number of ways in which first, second and third prizes will be awarded = 560

Step-by-step explanation:

\( \frac{1}{3x} + \frac{7}{ {x}^{2} } + \frac{x + 2}{x} \)

\( \frac{x}{ {3x}^{2} } + \frac{21}{3 {x}^{2} } + \frac{3 {x}^{2} + 6x}{3 {x}^{2} } \)

\( \frac{ {3x}^{2} + 7x + 21 }{ {3x}^{2} } \)

Choice D

Answer:

28

Step-by-step explanation:

Answer: D. Simple Random Sampling

Step-by-step explanation: When selection is made or based on chance which is equal or the same for all members within a population. In the scenario described above, there is no prior shuffling, arrangement or segregation of members within the population into groups or subgroups, rather the interviewed voters were chosen at random directly from within the larger population based on equal chance. Therefore voters already have their numbers, then using a random number generator, voters whose number corresponds were interviewed is a clear scenario of simple Random Sampling.

Using sampling concepts, it is found that the correct option is:

d. simple random sampling

Samples are classified as:

In this problem, a random number is generated to select each voter, hence it is a simple random sampling, and option d is correct.

To learn more about sampling concepts, you can take a look at https://brainly.com/question/25122507

Answer:correct answer is 0.57

5.71

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

3u^2 + 7u - 8 = 0

Now we can factor the quadratic:

(3u - 1)(u + 8) = 0

Therefore, either:

3cos(θ) - 1 = 0

cos(θ) = 1/3

or:

cos(θ) + 8 = 0

cos(θ) = -8 (not possible, since cos(θ) is between -1 and 1)

So, we have cos(θ) = 1/3. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse cosine function:

θ = arccos(1/3)

Using a calculator, we find:

θ ≈ 1.2309 or θ ≈ 5.1102

Therefore, in radians, the solutions for θ are approximately:

1.2309 (which is less than 2π)

5.1102 (which is greater than 2π)

So the only answer that satisfies 0 ≤ θ < 2π is:

1.2309 (rounded to four decimal places)

Therefore, the answer is:

0 0 8 8 16 16 16 16 20 24 24 24 28 32 32 32 40 40 48 48 56 72

Answer:

28. B

29. D

30. A

Step-by-step explanation:

28.

2 5/8 yd × 5/6 yd =

= 21/8 × 5/6 yd²

= 105/48 yd²

= 35/16 yd²

= 2 3/16 yd²

Answer: B

29.

2641 becomes 6241.

In 6241, the 6 is in the thousands place.

6 × 1000 = 6000

Answer: D

30.

90 + 7 × (7 - 1) =

Use the correct order of operations.

= 90 + 7 × 6

= 90 + 42

= 132

Answer: A

The length of a football pitch is 90 metres, correct to the nearest metre. Complete the error interval for the length of the football pitch is 0.5 meters.

There are different types of errors in mathematics. These include error intervals, systematic errors, rounding errors, and random errors. Error intervals are used to express the minimum and maximum possible values for a given measurement, or range of measurements.

According to the given question, the length of a football pitch is 90 metres, correct to the nearest metre. The nearest meter means that the length is within half a meter, both above and below the measurement, as 0.5m is half a meter. So, we can say that the error interval for the length of the football pitch is 0.5 meters.

Note that this means that the actual length of the football pitch could be anywhere from 89.5 meters to 90.5 meters, inclusive.

For more questions on: metres

https://brainly.com/question/1578784

#SPJ8

Answer:

Pollution was diluted

Step-by-step explanation:

The proof of ΔRUV ≅ ΔSUT is shown below.

Given that:

RSTV is a rectangle and U is the midpoint of VT.

Here, We have to Prove:

⇒ ΔRUV ≅ ΔSUT

Now, We can prove as;

Statement                               Reason

1) RSTV is a rectangle               Given

2) Angle V and T are                Because every angle in a rectangle is 90

right triangle.

3) ∠V ≅ ∠T                               Because both are right angle.

4) U is the midpoint of VT.        Given

5) VU = UT                                By midpoint theorem.

6) VR ≅ TS                                Opposite sides of rectangle.

7) ΔRUV ≅ ΔSUT                       By SAS congruency theorem.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Answer:

EF = 19

Step-by-step explanation:

EF = (23 + 15)/2 = 19

Answer:

y = \(\frac{4}{5}\) x + \(\frac{6}{5}\)

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 4, - 2) and (x₂, y₂ ) = (6, 6) ← 2 points on the line

m = \(\frac{6-(-2)}{6-(-4)}\) = \(\frac{6+2}{6+4}\) = \(\frac{8}{10}\) = \(\frac{4}{5}\) , then

y = \(\frac{4}{5}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (6, 6 ) , then

6 = \(\frac{24}{5}\) + c ⇒ c = \(\frac{30}{5}\) - \(\frac{24}{5}\) = \(\frac{6}{5}\)

y = \(\frac{4}{5}\) x + \(\frac{6}{5}\) ← equation of line

Answer: 118

Step-by-step explanation:

Angle ABC and Angle BCD add up to 180 degrees, because Line AB and line CD are parallel. Because of this, Angle BCD can be moved up the the angle above 3n-47. Because the two angles fall on to a straight line, we can say that (3n-47)+(n+7)=180. Solving, n=55, so angle ABC equals 118 degrees.

https://brainly.in/question/28196155#:~:text=Step%2Dby%2Dstep%20explanation%3A&text=1%20The%20corresponding%20angles%20are,alternate%20exterior%20angles%20are%20equal. See #5.

Answer:

The 95% confidence interval for the mean score, , of all students taking the test is

        \(28.37< L\ 30.63\)

Step-by-step explanation:

From the question we are told that

    The sample size is \(n = 59\)

    The mean score is  \(\= x = 29.5\)

     The standard deviation \(\sigma = 5.2\)

Generally the standard deviation of mean is mathematically represented as

                \(\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }\)

substituting values

               \(\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }\)

             \(\sigma _{\= x} = 0.677\)

The degree of freedom is mathematically represented as

          \(df = n - 1\)

substituting values

        \(df = 59 -1\)

        \(df = 58\)

Given that the confidence interval is 95%  then the level of significance is mathematically represented as

         \(\alpha = 100 -95\)

        \(\alpha =\)5%

        \(\alpha = 0.05\)

Now the critical value at  this significance level and degree of freedom is

       \(t_{df , \alpha } = t_{58, 0.05 } = 1.672\)

Obtained from the critical value table  

    So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as

      \(\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})\)

substituting value

      \((29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)\)

       \(28.37< L\ 30.63\)