I WILL GIVE BRANLY A librarian kept track of the kinds of books that boys and girls checked out in one day. Which graph best represents this data?

Answer:

3. Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.

Step-by-step explanation:

The domain of a function is the range of its inverse, and vice versa. The only answer choice that expresses this relationship is choice 3.

__

Comment on the answer choice:

The slope of the function is undefined at x=4, so restricting the function domain to the portion with positive slope means the domain restriction of the function is x > 4. That also means the range restriction of the function is y > 6. The domain restriction of the inverse function is the same: x > 6, not x ≥ 6. The answer choice has an error.

The domain of the original function with the positive slope is restricted to x > 4, and the range of f(x) is y ≥ 6. Therefore, the domain of the inverse function is x ≥ 6.

The function given is f(x) = |x – 4| + 6. When restricting the domain to the portion of the graph with a positive slope, the function increases. In the absolute value function, the slope changes at the vertex, which here is when x = 4. For x > 4, the slope is +1 because the graph of the function is increasing. So, considering the domain x > 4 makes the graph of the function only represent the portion with a positive slope.

The range of the original function with the restricted domain is f(x) ≥ 6, because the lowest value of |x – 4| is 0 when x ≥ 4, which results in f(x) = 0 + 6 = 6 when x = 4. Consequently, the corresponding range of the inverse function must be the domain of the original function, and thus, the domain of the inverse function must be x ≥ 6.

Answer:

The diameter of the largest pen you could build is [tex]\frac{100}{\pi }[/tex] or [tex]31.8309[/tex] ft

Step-by-step explanation:

As the equation for the circumference of a circle is

[tex]C=d\pi[/tex]

We can plug in the known value for C, which is 100 and solve for d

[tex]100=d\pi[/tex]

[tex]d=\frac{100}{\pi }[/tex]

ANSWER

The diameter of the largest pen you can build is 31.8 feet to the nearest tenth.

EXPLANATION

You have 100 feet of fencing to build a circular sheet pen.

The largest diameter you can get is when you use all the 100 feet of fencing to build the sheet pen.

The circumference of the circular sheet pen must then be 100 feet.

Then using the formula for circumference, we have:

C=πd

100=πd

[tex]d = \frac{100}{\pi} [/tex]

d=31.83 ft.

Answer: I would just say add a line to the Equal sign so the equation would read

5+5+5≠550, since this way it would say that 5+5+5 ISNT equal to 550 which is technically true, but that might be wrong.

Answer:

The principal of the loan is $350000

$26844 is not half 54886 so the statement is not true

Step-by-step explanation:

* Lets use the given rule to solve the question

- The total loan amount to be paid = p (1 + r)^t , where

# t is time in years,

# r is interest rate as a decimal

# p is the principal of the loan

- To find t divide the number of months by 12

∵ t = 30/12 = 2.5 years

∵ r = 6/100 = 0.06 ⇒ the interest rate in decimal

∵ The total loan amount to be paid = $404,886

∴ 404,886 = p (1 + 0.06)^2.5

∴ 404,886 = p (1.06)^2.5 ⇒ divide both sides by (1.06)^2.5

∴ p = 404,886 ÷ [(1.06)^2.5] ≅ $350,000

* The principal of the loan is $350,000

- To check the statement of the manager lets find the difference

  between the total loan amount and the principal

∵ The principal of the loan is $350,000

∵ the total loan amount to be paid is $404,886

∴ The difference = 404,886 - 350,000 = $54886

- Lets find the total loan amount to be paid when the interest rate

 was cut in half

∵ The total loan amount to be paid = p (1 + r)^t

∵ t = 30/12 = 2.5 years

∵ The half of 6% is 3%

∴ r = 3/100 = 0.03 ⇒ the interest rate in decimal

∵ p = $350,000

∴ The total loan amount to be paid = 350,000 (1 + 0.03)^2.5

∴ The total loan amount to be paid = 350,000 (1.03)^2.5

∴ The total loan amount to be paid = $376,844

- Lets find the difference between the total amount to be paid and

 the principal

∴ The difference = 376,844  - 350,000 = $26844

∵ $26844 is not half 54886

* The statement is not true

The answer is:

The second option,

b.) [tex]C(x)=40.60x+201[/tex]

We are given the functions E(x) and K(x), since they both are function of the same variable, we need to add them in order to find the correct option.

From the statement we know the functions:

[tex]E(x)=22.75x+74[/tex]

and

[tex]K(x)=17.85x+127[/tex]

So, adding the functions we have:

[tex]C(x)=E(x)+F(x)[/tex]

[tex]C(x)=(22.75x+74)+(17.85x+127)[/tex]

[tex]C(x)=22.75x+17.85x+74+127[/tex]

[tex]C(x)=40.60x+201[/tex]

Hence, the answer is the second option,

b.) [tex]C(x)=40.60x+201[/tex]

Have a nice day!

Answer:

The answer is b

Step-by-step explanation:

C(x)=40.60x + 201

21.6 x 5.9 x 0.5 = 63.72

The area of the triangle is 63.72 ft²

Answer:

63.72 ft^2

Step-by-step explanation:

The base and the height of the triangle are given:  21.6 ft and 5.9 ft.

Apply the area-of-a-triangle formula:

A = (1/2)(base)(height)

Here, the area is

A = (1/2)(21.6 ft)(5.9 ft) = 63.72 ft^2

The equation of the line that passes through (5,-2) and (-3,4) is y = (-3/4)x + 7/4.

To find the equation of the line that passes through (5,-2) and (-3,4), we can use the formula for the equation of a straight line, which is y = mx + b.

Answer:

it is C

Step-by-step explanation:

i hope this helped = ) <3

You can find length by knowing the formula for perimeter: 2l+2w= p; where l= length, w= width, and p= perimeter. Substitute the things you know and solve.

In this case, the length would be 11 feet.

Answer:

x = -48, y = 25

Step-by-step explanation:

Both equations have a 5y term, we can work with that.

Let's first convert them into 5y = ... form:

2x + 5y = 29 => 5y = 29 - 2x

3x + 5y = -19 => 5y = -3x - 19

Now we can equate the right-hand sides:

29 - 2x = -3x - 19

And simplify:

29 + 19 = -3x + 2x => x = -48

Let's put this x value in the first:

2*(-48) + 5y = 29 =>

-96 - 29 = -5y =>

-5y = -125 =>

y = 25

Answer:

3C + 5 T = 550

C+T= 122

PUT IN 1  T= 122-C

3C + 5 (122-C)=550

3C -5C + 610=550

-2C= 550 - 610= -30

C= 15

T= 122-15 = 107

Step-by-step explanation:

Answer:  50

Step-by-step explanation:

Let x be the number of cars and y be the number of trucks .

By considering the given information, we get

[tex]x+y=122-----------------(1)\\\\3x+5y=510-------------------(2)[/tex]

Multiply (1) by 3 , we get

[tex]3x+3y=366--------------(3)[/tex]

Eliminate equation (3) from (2), we get

[tex]2y=144\\\\\Rightarrow\ y=72[/tex]

Put y= 72 in equation (1), we get

[tex]x+72=122\\\\\Rightarrow\ x=122-72=50[/tex]

Hence, the number of cars did the club = 50

The collection of investments in a mutual fund is referred to as a portfolio, which can include a variety of stocks and bonds. Index funds are examples of mutual funds that track the performance of market indexes. Mutual funds are significant in the financial landscape, with many U.S. households investing in them.

The collection of investments in a mutual fund is called a portfolio.

Mutual funds gather stocks or bonds from various companies into one investment vehicle, making it simpler for investors to own a diversified collection without purchasing each security individually.

Investors purchase shares of the mutual fund and receive returns based on the collective performance of the fund's portfolio.

For instance, index funds are types of mutual funds that aim to mimic the performance of a specific market index.

This strategy offers broad market exposure and low operating expenses.

There are also specialized mutual funds that focus on particular sectors or regions, offering different levels of risk and potential return.

In the modern financial landscape, mutual funds play a significant role, with a substantial percentage of U.S. households holding investments in these funds.

Answer:

[tex]\frac{7\pi }{2}[/tex]

Step-by-step explanation:

Given

sin x = - 1

x = [tex]sin^{-1}[/tex] ( - 1 )

  = [tex]\frac{3\pi }{2}[/tex] + 2kπ k ∈ Z

For 2π < x < 4π, then

x = [tex]\frac{7\pi }{2}[/tex]

Answer:

The safe dose for the child is:   [tex]640\ \frac{mg}{day}[/tex]

Step-by-step explanation:

We know that the conversion factor is 40 mg/kg/day

The child weighs 16 kg. This means that 40 mg per day corresponds to each kilogram of the child.

So to know how many milligrams per day correspond per day we must multiply 16 kg by the conversion factor

[tex]16\ kg * 40\ \frac{\frac{mg}{kg}}{day} = 640\ \frac{mg}{day}[/tex]

Answer:

The safest dose would be 640 mg per day.

Hope this helps!

Answer:

x = π/2 or

x = π/2 + 2πn (for any value of n)

Step-by-step explanation:

We need to find the numerical value of the trigonometric function sinx+1/sinx=1+cscx

Subtract 1+cscx on both sides

sinx + 1/sinx -(1+csc x) = 1+cscx - (1+cscx)

sinx + 1/sinx -1 -csc x = 0

Taking LCM i.e, sinx and solving

(sinx)(sinx) + 1 - sinx -cscx(sinx) / sinx = 0

Multiplying sinx on both sides

sin^2 x + 1 -sinx - cscx(sinx) =0

as we know, cscx = 1/ sinx

sin^2 x + 1 -sinx - (1/sinx)(sinx) = 0

Solving,

sin^2 x + 1 -sinx - 1 = 0

sin^2 x - sin x =0

Let u = sinx

Putting it in above equation

u^2 - u =0

Solving the equation:

u= 1 , u= 0

Putting back the value of u

sin(x) = 1 and sin(x) = 0

x = sin ⁻¹ (1) and x = sin ⁻¹ (1) =0

x = 90° or π/2 and x = 0 (undefined for the question)

So, x = π/2 or

x = π/2 + 2πn (for any value of n)

Answer:

Subtract the flat fee from the total amount, then divide that amount by the cost per mile.

89 - 44 = 45

45 / 0.24 = 187.5 miles total.

Answer:

±i√55

Step-by-step explanation:

Answer:

x = - [tex]\frac{1}{4}[/tex], x = 2

Step-by-step explanation:

Given

8x² - 14x - 4 = 0 ( divide through by 2 to simplify )

4x² - 7x - 2 = 0

To factorise the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 4 × - 2 = - 8 and sum = - 7

The factors are - 8 and + 1

Use these factors to split the x- term

4x² - 8x + x - 2 = 0 ( factor the first/second and third/fourth terms )

4x(x - 2) + 1(x - 2) = 0 ← factor out (x - 2) from each term

(x - 2)(4x + 1) = 0

Equate each factor to zero and solve for x

4x + 1 = 0 ⇒ 4x = - 1 ⇒ x = - [tex]\frac{1}{4}[/tex]

x - 2 = 0 ⇒ x = 2

Answer:

1.  $640

2. About 10.3 years later

Step-by-step explanation:

This is a compound decay problem. The formula is

[tex]F=P(1-r)^t[/tex]

Where

F is the future amount

P is the initial amount

r is the rate of decrease (in decimal), and

t is the time in years

Question 1:

We want to find F after 2 years of a phone initially costing 1000. So,

P = 1000

r = 20% or 0.2

t = 2

plugging into the formula, we solve for F:

[tex]F=P(1-r)^t\\F=1000(1-0.2)^2\\F=1000(0.8)^2\\F=640[/tex]

The phone is worth $640 after 2 years

Question 2:

We want to find when will the phone be worth 10% of original.

10% of 1000 is 0.1 * 1000 = 100

So, we want to figure this out for future value of 100, so F = 100

We know, P = 1000 r = 0.2 and t is unknown.

Let's plug in and solve for t (we need to use logarithms):

[tex]F=P(1-r)^t\\100=1000(1-0.2)^t\\100=1000(0.8)^t\\\frac{100}{1000}=0.8^t\\0.1=0.8^t\\ln(0.1)=ln(0.8^t)\\ln(0.1)=t*ln(0.8)\\t=\frac{ln(0.1)}{ln(0.8)}\\t=10.32[/tex]

So, after 10.32 years, the phone would be worth less than 10% of original value.

Answer:

Step-by-step explanation:

[tex]Q+p+Q+p+Q\\\\\text{combine like terms}\\\\=(Q+Q+Q)+(p+p)=3Q+2p[/tex]

ANSWER

1. -7

2. no real solution

EXPLANATION

1. The given quadratic equation is:

[tex]12 {x}^{2} - 7x - 9 = 0[/tex]

Comparing this to

[tex]a{x}^{2} + bx + c= 0[/tex]

we have a=12, b=-7 and x=-9.

Therefore the value of b is -7

2. The given quadratic equation is

[tex]3{x}^{2} + 3x + 2= 0[/tex]

We have a=3,b=3 and c=2.

The discriminant of this equation is

[tex]D= {b}^{2} - 4ac[/tex]

[tex]D= {3}^{2} - 4(3)(2)[/tex]

[tex]D= 9- 24 = - 15[/tex]

Since the discriminant is negative, the equation has no real roots.

[tex]12x ^{2}-7x -= 0 \\ \\ x = \frac{7 + \sqrt{481} }{24} \: or \: x = \frac{7 - \sqrt{481} }{24} \\ \: b. \: -7 \\ \\3x^{2} + 3x + 2 = 0 \\ c. \: no \: real \: solutions[/tex]

Answer:

Step-by-step explanation:

x% of y equals to 0.01*x*y

Just put the numbers in the formula

33% of 507 = 167.31

48% of 375 = 180

76% of 285 = 216.6

60% of 398 = 238.8

89% of 150 = 133.5

26% of 430 = 111.8

81% of 216 = 174.96

5% of 584 = 29.2

18% of 725 = 130.5

2% of 115 = 2.3

90% of 152 = 136.8

12% of 649 = 77.88

55% of 216 = 118.8

43% of 108 = 46.44

97% of 235 = 227.95

Answer:

x < 6

Step-by-step explanation:

Let's isolate x first.  Add 3 to both sides, obtaining (1/3)x < 2.  Now multiply both sides by 3 to eliminate the fraction:  x < 6

Answer: 0, 4, -9

Set the equation equal to zero.

x(x - 4)(x + 9) = 0

Solve for x by setting each factor equal to zero.

The factors in the equation are x, (x - 4), and (x + 9).

        x = 4

        x = -9

The zeros of the function are 0, 4, and -9.

Answer:

Step-by-step explanation:

Convert the fractions to the decimals (you can use the calculator):

2/3 = 2 : 3 = 0.6666...

3/5 = 3 : 5 = 0/6

We have

0.65

0.666...

0.6

0.5

The order from least to greatest:

0.5

0.6

0.65

0.666..

[tex]\begin{array}{c|c|c|c|c}0&.&5\\0&.&6\\0&.&6&5\\0&.&6&6&6...\end{array}[/tex]

Answer:

all real numbers greater than or equal to 3

Step-by-step explanation:

There's some ambiguity in your "3/x+2-sqrt x-3."  I will assume that you meant:

   3

---------- - sqrt(x - 3).       Using parentheses often changes everything.

 x + 2  

Here we see that x cannot = -2, because x + 2 would be zero then.  And x must be greater than or equal to 3, so that the input to the sqrt function will be 0 or greater.  The domain for f(x) is all real numbers greater than or equal to 3.  The prohibition against x = -2 has no bearing on the overall domain of this function.

Answer:

The domain for f(x) is all real numbers GREATER than or equal to 3

Step-by-step explanation:

Let's do the same thing to evaluate g(-5):

-5Answer:

Step-by-step explanation:

Never heard of "synthetic substitution."  I think you meant "synthetic division," which is a great method of evaluating polynomials for given input values.

g(x) = x^5 – 8x^3 – 2x + 7 is missing two terms.

With all terms showing, it would read:

g(x) = x^5 – 0x^4 + 8x^3 – 0x^2 - 2x + 7.  The coefficients are {1, 0, 8, 0, -2, 7}.

Let's evaluate g(3).  Use 3 as divisor in synth. div.:

3   )  1   0   8   0   -2   7

            3   9  51  153 453

    ------------------------------

       1    3   17  51  151  460      Since the remainder is 460, the value of g(3) is also 460.

-5  )   1    9    8    0    -2       7

              -5  -20  60 -300 1510

    ----------------------------------

       1      4    -12   60 -302   1517

The remainder is 1517, and so g(-5) = 1517.

Answer:

28, -2,108

Step-by-step explanation:

Answer:b

Step-by-step explanation:

ANSWER

x=100,y=10

EXPLANATION

The given logarithmic equations are;

[tex] log_{10}( {x}^{2} {y}^{3} ) = 7[/tex]

This implies that,

[tex] {x}^{2} {y}^{3} = {10}^{7} ...(1)[/tex]

and

[tex] log_{10}( \frac{x}{y} ) = 1[/tex]

This implies that,

[tex] \frac{x}{y} = {10}^{1} [/tex]

[tex]x = 10y...(2)[/tex]

Put equation (2) into equation (1)

[tex]{(10y)}^{2} {y}^{3} = {10}^{7}[/tex]

[tex]10 ^{2} y^{2} {y}^{3} = {10}^{7}[/tex]

[tex]{y}^{5} = {10}^{5}[/tex]

Hence y=10.

This implies

[tex]x = 10(10) = 100[/tex]

Answer:

C

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

Note the 2 legs are equal, that is both x, hence

x² + x² = 16²

2x² = 256 ( divide both sides by 2 )

x² = 128 ( take the square root of both sides )

x = [tex]\sqrt{128}[/tex] = [tex]\sqrt{64(2)}[/tex] = [tex]\sqrt{64}[/tex] × [tex]\sqrt{2}[/tex] = 8[tex]\sqrt{2}[/tex]