Need help with this question please

Answer: The inverse of the function f(x)  = 4(x-3)² + 2 is

The given function is:

f(x)   =  4(x  - 3)²  +  2

To find the inverse of the function:

Make x as the subject of the formula

Replace x by  and replace f(x) by x

Therefore, the inverse of the function is:

Step-by-step explanation:

The value of x is (5t-a) when the formula is 6x+a=5(x+t).

According to the question,

We have the following information:

6x+a=5(x+t)

Now, from this formula, we have to mark the value of x or in other words, we have to find the value of x.

Now, multiplying 5 into the bracket on the right hand side:

6x+a = 5x+5t

Subtracting 5x from both sides of the equation:

6x-5x+a = 5t

x+a = 5t

Subtracting a from both sides of the equation, we will get the final value of x in terms of t and a:

x = 5t-a

Hence, the value of x is (5t-a) when the formula is 6x+a=5(x+t).

To know more about value here

https://brainly.com/question/4806080

#SPJ9

Answer:

£600

Step-by-step explanation:

Katie gives 1/3 of the money to her sister.

1/3 of 1200 is 400, because 1200 divided by 3 is 400. So she gives 400 to her sister, which means she has 1200-400= 800 left.
When she gives 1/4 of the remaining to her brother, that means that we need to figure out how much 1/4 of 800 is. 800 divided by 4 is 200. So Katie gives 200 to her brother.

800 that she has remaining minus the 200 she gives to her brother leaves her with 800-200 = 600

His new grade will be 85.838 , this can be calculated using simple fraction.

What is fraction?

As the components of a whole, fractions are by definition. The entire can be a single item or a collection of items.

Main Body:

Initial percentage of child = 93.73%

Child's percentage at test = 74%

according to the question his 40% of test grade is accounted

Parts of grade is from test = 4/10

So his new grade = (4/10)*74 + (6/10) *93.73

New grade = 29.6 +56.238

Hence the new grade for the child will be 85.838%

To learn more about fraction click on the link below.

https://brainly.com/question/78672

#SPJ13

Answer:

k=5

Step-by-step explanation:

15-8k+15k-8=42

15+7k=50

7k=35

k=5

Answer:

The value of k is 1.

Step-by-step explanation:

Answer:

The value of k=1

Step-by-step explanation:

According to the ratio, it doesn't make sense to have a total of 9 people in the dance competition.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

The ratio of boys to every girls is 3:2 in a dance competition.

Let's find if it will make sense to have a total of 9 people in the competition.

Therefore,

number of boys = 3 / 5 × 9 = 27 / 5 = 5.4

number of girls = 2 / 5 × 9 = 18 / 5 = 3.6

Therefore, it doesn't make sense to have 9 people in the competition because the actual number of boys and girls will be in decimal which is impossible.

learn more on ratio here: https://brainly.com/question/26953234

#SPJ1

Target buys masks wholesale for $15 a piece. They mark them up 150% for resale. If Kara bought one from them and paid 12% sales tax, then

The amount spent by Kara overall is $42.

Here, we need to determine how much money she spent overall. Finding the mask’s cost after adding the 150% mark is the first step in determining how much is spent.

She purchased it for $37.5 but had to pay 12% tax on it. Consequently, she spent $42 total.

Use proportional relationships to solve multi step ratio and percent problems. Examples include simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

To learn more about proportional relationships click here: https://brainly.com/question/10424180

#SPJ4

[tex]\frac{5}{3}[/tex]The point on the number line to plot the point which is opposite [tex]\frac{5}{3}[/tex] is [tex]\frac{-5}{3}[/tex]

A number line is a horizontal representation of a number of parts with equal intervals.

What exactly is a number line?

A number line is a horizontal line with evenly spaced numerical increments. It shows how to answer plotted the number on the line.

If two numbers are the same distance from 0 and on opposite sides of the number line, they are opposites.

For example, 4 is the inverse of -4, and -4 is the inverse of 4. They are both equal distances from zero.

Given: number is [tex]\frac{5}{3}[/tex]

The opposite of 5/3 is the additive inverse let x be the additive inverse

[tex]\frac{5}{3}[/tex] + x = 0

x = 0 - [tex]\frac{5}{3}[/tex]

x= - [tex]\frac{5}{3}[/tex]

To learn more about number lines visit:

https://brainly.com/question/27114736

#SPJ4

Answer:

Step-by-step explanation:

Move all terms not containing xx from the center section of the inequality.

Inequality Form:

0<x<30<x<3

Interval Notation:

(0,3)

Answer:

y=-4

x=-3

Step-by-step explanation:

x=3y/4

5*(3y/4) +6y+39=0

15y/4+6y+39=0

3.75y+6y+39=0

9.75y=-39

y=-4

x=-3

Answer:

x = 2 , y = 29

Step-by-step explanation:

if the quadrilateral is to be a parallelogram , then

• opposite sides are congruent

• opposite angles are congruent

Then

2x + 9 = x + 11 ( subtract x from both sides )

x + 9 = 11 ( subtract 9 from both sides )

x = 2

and

3y + 19 = 106 ( subtract 19 from both sides )

3y = 87 ( divide both sides by 3 )

y = 29

Answer:

50

Step-by-step explanation:

Since 45-45-90 tri, x^2+x^2=100^2

So 2x^2=10000

2x=100 and x=50

Answer:

a = 70.71068 = 50√2

Step-by-step explanation:

a = √c^2 - b^2

= √1002 - 70.7106781186552

= √5000

= 70.71068 = 50√2

Thanks.

The amount Gabriela paid with the discount is $50.4.

Discount is a reduction in price. Discount means reducing the price or value of an object or item.

Gabriela bought a new pair of glasses at the store when they were 30% off the sale.

The regular price of the glasses is 72 dollars. The amount Gabriela paid with the discount can be calculated as follows:

discount = 30% off of the sale

discount = 30 / 100 × 72

discount = 2160/ 100

discount = 21.6 dollars

Therefore,

price paid with the discount = 72 - 21.6

price paid with the discount = 50.4 dollar

Therefore, the amount she paid with the discount is 50.4 dollars

learn more on discounts here: https://brainly.com/question/8462955

#SPJ1

The solutions to this system of linear equation 3x−2y=14 is ( [tex]\frac{2y + 14}{3}[/tex] ,   [tex]\frac{3x}{2}[/tex]-7).

Add 2y to both sides.

3x=14+2y

The equation is in standard form.

3x=2y+14

Divide both sides by 3.

[tex]\frac{3x}{3}[/tex] = [tex]\frac{2y + 14}{3}[/tex]

Dividing by 3 undoes the multiplication by 3.

x = [tex]\frac{2y + 14}{3}[/tex]

​Now,

3x−2y=14

Subtract 3x from both sides.

−2y=14−3x

Divide both sides by −2.

[tex]\frac{-2y}{-2}[/tex] = [tex]\frac{14 - 3x}{-2}[/tex]

Dividing by −2 undoes the multiplication by −2.

y =  [tex]\frac{14 - 3x}{-2}[/tex]

Divide 14−3x by −2.

y = [tex]\frac{3x}{2}[/tex] - 7

Learn more about Linear equation here;

https://brainly.com/question/2030026

#SPJ4

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 12 +4}{2}~~~ ,~~~ \cfrac{ -4 +9}{2} \right) \implies \left(\cfrac{ 16 }{2}~~~ ,~~~ \cfrac{ 5 }{2} \right)\implies \left( 8~~,~~2\frac{1}{2} \right)[/tex]

The inequality for the number of monthly calls for which Plan 1 is more economical than Plan 2 is,

x > 320.

And x > 320  means that the monthly calls should be more than 320, for Plan 1 to be more economical than Plan 2.

(a) Given, that the telephone company offers two billing plans for local calls. Plan 1 charges ​$35 per month for unlimited calls.

Plan 2 charges ​$19 per month plus ​$0.05 per call.

Let x calls be made,

Now, according to the Plan 1,

the charges for 'x' calls be ​$35 only

according to the Plan 2,

the charges for 'x' calls be

​$19 + $0.05x

Now, Plan 1 is more economical than Plan 2 for,

$35 < ​$19 + $0.05x

On solving the inequality, we get

$16 < $0.05x

On dividing both the sides by 0.05, we get

16/0.05 < x

320 < x

i.e. the monthly calls be more than 320.

(b) Now, as in part (a) we got,

320 < x

which means that the monthly calls should be more than 320, for Plan 1 to be more economical than Plan 2.

Hence, theinequality for the number of monthly calls for which Plan 1 is more economical than Plan 2 is,

x > 320.

And x > 320  means that the monthly calls should be more than 320, for Plan 1 to be more economical than Plan 2.

Learn more about Linear Inequality here https://brainly.com/question/28418226

#SPJ1

The factor of the expression is [tex]49x^8-16y^{14} =(7x^4-4y^7)(7x^4+4y^7)[/tex].

What is factor?

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

Given, 49x⁸ − 16y¹⁴ is an expression.

We can write it as  (7x⁴)² − (4y⁷)²

we know, [tex]a^2-b^2=(a-b)(a+b)[/tex]

using this identity, we get

49x⁸ − 16y¹⁴ =  (7x⁴ - 4y⁷)(7x⁴ + 4y⁷)

To know more about factor, visit:

https://brainly.com/question/17010373

#SPJ9

The equation to describe the information that 2 less than 4 times x is 4x - 2.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, 2 less than 4 times will be:

= (4 × x) - 2

= 4x - 2

Therefore, the equation is 4x - 2.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Step-by-step explanation:

5.

normally no.

just think - we are talking about people. it's it possible to have half of a friend at a game ?

no, the input is not possible.

but if this function is used in the context or a larger analysis, and mean values are created and checked, then it might be valid.

it all depends on the context of how the function is used.

2.

we don't see all answer options, but the range is the interval or set of all valid y-values (the 2nd number in an ordered pair).

we see : -1, 3, 4, 6

whichever answer option shows this is correct.

Answer:

1

Step-by-step explanation:

Change is y over the change in x

The y's are 4 and 7.

The x's are -1 and 2

[tex]\frac{4-7}{-1-2}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1

Answer:

no

Step-by-step explanation:

\frac{1}{6}f^3a=

6

1

​

\frac{1}{6}f^3a=

6

1

​

f

3

a=

\,\,D

D

The graph of f(x) = (3/4)ˣ is attached. The values are f(-2) = 16/9, f(-1) = 4/3, f(0) = 1, f(1) = 3/4 and f(2) = 9/16

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the exponential function:

f(x) = (3/4)ˣ

Hence:

f(-2) = (3/4)⁻² = 16/9

f(-1) = (3/4)⁻¹ = 4/3

f(0) = (3/4)⁰ = 1

f(1) = (3/4)¹ = 3/4

f(2) = (3/4)² = 9/16

The graph of f(x) = (3/4)ˣ is attached.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

3

Step-by-step explanation:

0.9660  is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

  If the number of tablets in a shipment is sufficiently large, we can consider the testing procedure you describe (selecting a random sample of 29 ibuprofen tablets and counting the number of defective tablets in the sample) to be a binomial probability experiment.  

Let X = (Number of defective ibuprofen tablets in a random sample of 29 tablets.)  Then we may reasonably assume that X follows a binomial distribution.  For each "trial" (that is, each tablet selected), there are two possible outcomes, "success" (the tablet is defective), or "failure" (the tablet is not defective).  Note that the word success as used in the binomial distribution does not carry the connotation of being a "good" outcome.  A "success" is simply the outcome you are interested in counting, which in this case is the number of defectives in the sample.  The important parameters for a binomial distribution are n (the number of trials) and p (the probability of success on any one trial.)   For this situation, we have p = .01 (since we are told 1% of the tablets in the shipment are defective) and n = 29.  The general formula for the binomial distribution is

P(x) = nCx·px·(1 - p)n-x

where x is the number of successes in n trials (In this problem, x is the number of defectives in a random sample of 29 tablets.)  The symbol nCx is the "number of combinations of n things taken x at a time". This is the number ways of choosing x distinct objects from a set of n objects, without regard to order. It is given by

nCx = n!/[x!·(n-x)!]

where ! is the factorial symbol.

We want to find the probability that the shipment is accepted.  We are told that a shipment will be accepted if at most one tablet doesn't meet the required specifications.  That is, the number of defectives must be less than or equal to one.

P(Shipment accepted) = P(X ≤ 1).  (In this case, X ≤ 1 if and only if X=0 or X=1)= P(0) + P(1).

So we calculate P(0) (the probability of 0 defective tablets in the shipment), and P(1) (the probability of 1 defective.)  Using the formula for the binomial distribution, we have

P(0) = 29C0·(.01)0·(1 - .01)29 - 0.

But 29C0 = 1, so

P(0) = 1·(.01)0·(.99)29 ≅ .74717

Also,

P(1) = 29C1·(.01)1·(1 - .01)29 - 1.

Calculating 29C1, we have

    29C1 =  29!/[1!·(29-1)!] = 29, so

          P(1) = 29·(.01)1·(99)28

          P(1) ≅ .21887

Finally, then, we have

P(Shipment accepted) ≅ .74717 + .21887 ≅ .9660 (to 4 decimal places.)

learn more about probability here :

brainly.com/question/11234923

#SPJ4

Answer:  an = 18 - 3n

Step-by-step explanation:

so the next term should be 3

Answer:

  $951.74

Step-by-step explanation:

You want the future value of $750 earning 3% per year for 8 years, compounded semi-annually.

The value of an account earning interest at rate r on principal P compounded n times per year for t years is ...

  A = P(1 +r/n)^(nt)

For P=750, r=0.03, n=2, t=8, this is ...

  A = 750(1 +0.03/2)^(2·8) = 750(1.015^16) ≈ 951.74

The account will be worth about $951.74 in 8 years.

__

Additional comment

All spreadsheets and many graphing calculators have the necessary financial functions for computing this value. Apps are available for the purpose, as well.

Answer:

Step-by-step explanation:

Step-by-step explanation:

What is the value?

Please put the full question

Then only I would be able to help you