\(9(x+1) -4x = 5-(x-3)\)

1. The domain for which function is one-to-one and non-decreasing [3, ∞).

2. The inverse function in the domain g(x) = √x + 3

To find a domain on which f is one-to-one and non-decreasing, we need to ensure that the function is increasing or non-decreasing (i.e., it is always moving in the positive x direction) and that each value of x maps to a unique value of f(x). A function is one-to-one if it passes the horizontal line test, meaning that every horizontal line intersects the graph at most once.

1. The function f(x) = (x-3)² has a minimum value of zero at x=3, and is   increasing on the interval (-∞, 3) and (3, ∞).

Therefore, the domain on which f is one-to-one and non-decreasing is [3, ∞).

2. To find the inverse of f restricted to this domain, we can first solve for x in terms of f(x):

f(x) = (x-3)²

√f(x) = x-3 (we take the positive square root since we're restricted to the non-negative range of f(x))

x = √f(x) + 3

Now we can define the inverse function g(x) as:

g(x) = √x + 3, where x is in the range [0, ∞).

Note that we have restricted the range of g(x) to [0, ∞) since the function f(x) is non-negative for all values of x, and therefore the inverse function must also be non-negative.

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The sides of the right triangle are:

a) AC

b) CB

c)  AB

We have the diagram of a right triangle, and we want to identify the side that is opposite to angle B.

That would be the side that does not intercept the vertex B, so it is AC.

Then we want to get the adjacent side to B that is not the hypotenuse.

That would be the side that intercepts vertex B and intercepts the vertex with the small red square, it is CB.

Finally, the vertex is the side opposite to the small red square (90° angle) so it is AB.

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9514 1404 393

Answer:

Step-by-step explanation:

The given relations tell you the side lengths form an arithmetic sequence with a common difference of 2.

  short side

  long side = short side + 2

  hypotenuse = long side + 2

__

There is only one "Pythagorean triple" that is an arithmetic sequence. The reduced form is (3, 4, 5). The numbers in this triple have a common difference of 1, so your side lengths will be double these values:

  shorter leg: 6 inches

  longer leg: 8 inches

  hypotenuse: 10 inches

_____

Alternate solution

As you can see, it is worthwhile to remember some Pythagorean triples. If you write an equation using the Pythagorean theorem, you can let s represent the short side.

  s^2 +(s+2)^2 = (s+4)^2

  2s^2 +4s +4 = s^2 +8s +16

  s^2 -4s -12 = 0 . . . . . . . subtract (s^2 +8s +16) to put in standard form

  (s -6)(s +2) = 0 . . . . . .  factor

  s = 6 or -2 . . . . . . . . . . values that make the factors zero

The only reasonable solution here is s=6.

The short side is 6", the longer side is 8", and the hypotenuse is 10".

Answer:

$54925

Step-by-step explanation:

Monthly Rent = 803

Number of apartments = 60

Kelly's commission = 9.5% -> 9.5/100 = 0.095

So

803*60*0.095 = ?

4577.10 per month.

12 months in a year

4577.10 * 12 = $54925.20

Rounded to nearest whole dollar 54925

Kelly makes $54925 per year

The matrix is 3 × 3 square matrix . Its values are:

\(a_{11} = 50 \\ a_{12} = 44 \\a_{13} = -43 \\a_{21} = 31 \\a_{22} = 16 \\a_{23} = 7 \\a_{31} = 37 \\a_{32} = 119 \\a_{33} = 94\)

Given,

Matrix A and Matrix B

Now,

According to matrix multiplication rule first row of one matrix will be multiplied with first column of second matrix if the columns in first matrix is equal to the rows of second matrix.

So,

Apply multiplication rule,

\(a_{11} = 30 + 14 + 6 = 50 \\ a_{12} = 55 + 7 - 18 = 44 \\a_{13} = -20 -35 + 12 = -43 \\a_{21} = 24 - 2 + 9 = 31 \\a_{22} = 44 -1 -27 = 16 \\a_{23} = -16 + 5 + 18 = 7 \\a_{31} = 36 + 16 - 15 = 37 \\a_{32} = 66 + 8 + 45 = 119 \\a_{33} = -24 -40 -30 = -94\)

Thus the values of the matrix can be calculated.

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Answer:

A

Step-by-step explanation:

hope this helps! :) Hope you have. a great day

Answer:

\(S_{15} = 299593\)

Step-by-step explanation:

Given

\(262144,\ 32768,\ 4096,\ 512; ...\)

Required

Determine the 15th partial sum

The nth partial sum of a geometric series is:

\(S_n = a* \frac{1 - r^n}{1 - r}\)

In this case:

\(a = 262144\)

\(n = 15\)

r is calculated as:

\(r = \frac{32768}{262144}\)

\(r = 0.125\)

Substitute values for a, r and n in \(S_n = a* \frac{1 - r^n}{1 - r}\)

\(S_{15} = 262144* \frac{1 - 0.125^{15}}{1 - 0.125}\)

\(S_{15} = 262144* \frac{1}{0.875}\)

\(S_{15} = \frac{262144* 1}{0.875}\)

\(S_{15} = \frac{262144}{0.875}\)

\(S_{15} = 299593.142857\)

\(S_{15} = 299593\) -- approximated

Answer:

The worst-case probability is 0.05

Step-by-step explanation:

The given significance level (\(\alpha\)) = 0.05

since Probability of a type I error is \(\alpha\)

∴ P (type I error) = 0.05

0.05 will be the worst-case probability of a type I error in at least one of the tests.

Answer:

KL = 7, so B is the correct answer.

Answer:

60

Step-by-step explanation:

\(a+b+c=180\\\frac{b+c}{2}=a \rightarrow b+c=2a\\\\a+2a=180\\3a=180\\a=60\)

Therefore, the value of a is 60 degrees

Answer:

1 / 0.9

2/ 0.12

3/ 0.2

4/ 0.07

5/ 0.8

6/ 0.72

7/ 0.47

8/ 0.6

9/ 0.02

10/ 0.96

Step-by-step explanation:

Answer:

1. 9/10

2. 12/100 - 3/25  

3. 2/10 - 1/5

4. 7/100

5. 8/10 - 4/5

6. 72/100 - 18/25

7. 47/100

8. 6/10 - 3/5

9. 2/100 - 1/50

10. 96/100 - 24/25

I simplified some of them.

Hope this helped and Brainliest please

Answer:

The correct answer is B.

Approximately 200 students received a test score between 70.5 and 80.

Answer:

El resto es 9.

Step-by-step explanation:

En una división el cociente es el resultado que se obtiene, el divisor es el número por el que se divide otro número, el dividendo es el número que va a dividirse entre otro y el resto es lo que queda cuando un número no puede dividirse exactamente entre otro. De acuerdo a esto, la división planteada se encuentra en la imagen adjunta donde al resolverla se encuentra que el número que queda es 9 y este es el resto.

Answer:

Step-by-step explanation:

I and II

Pages in a book and leaves on a tree can be counted precisely. They are discrete.

The height of a person cannot be measured exactly. We can get very good

approximations (to a lot of decimal places) but never exact. This is continuous.

Answer:

7/10

Step-by-step explanation:

solve 5 divide by 7 =0.714

solve 7 divided by 8 = 0.875

11 divided by 15 = 0.73333

7 divided by 10= .70

Answer:

$33

Step-by-step explanation:

Let the amount of money Corey has be $x.

Amount of money Bryce have= $(x +16)

Total amount= $50

$x +$(x +16)= $50

2x +16= 50

2x= 50 -16

2x= 34

Divide both sides by 2:

x= 34 ÷2

x= 17

Amount of money Bryce have

= $(17 +16)

= $33

The area of the triangle is 47.91 units²

When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.

Heron’s formula is:

Area =√s(s−a)(s−b)(s−c)

where,

a, b, c are the side length of the triangle

s is the semi-perimeter. s = (a+b+c)/2

In this case:

Using the knowledge of the radius of a circle. We can say:

a = BC = 3 + 9 = 12 units

b = AC = 5 + 3 = 8 units

c = AB = 5 + 9 = 14 units

s = (a+b+c)/2

s = (12+8+14)/2

s = 34/2

s = 17 units

Area = √s(s−a)(s−b)(s−c)

Area = √17(17−12)(17−8)(17−14)

Area = √17(5)(9)(3)

Area = √2295

Area = 47.91 units²

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Answer:

\(-\frac{11}{6}\ \frac{inches}{second}\)

Step-by-step explanation:

Rate of Change

The average velocity is defined as the rate of change of the distance with respect to time. The table shows the distances of an object as a function of time.

It's required to find the average velocity between 8 s and 20 s.

The rate of change can be approximated as the slope between two points. We take from the table the points (8,32) and (20,10) and calculate the slope.

The slope can be calculated with the equation:

\(\displaystyle v=\frac{d_2-d_1}{t_2-t_1}\)

\(\displaystyle v=\frac{10-32}{20-8}=\frac{-22}{12}\)

Simplifying:

\(\displaystyle v=-\frac{11}{6}\)

Choice: B. \(\mathbf{-\frac{11}{6}\ \frac{inches}{second}}\)

Answer: 224

Step-by-step explanation:

The total degrees of a 7-sided shape is 900. You can find that out using the equation (n-2) times 180. Where n is the number of sides. If you add up all the interior angles they equal 676. Then just subtract 676 from 900. 900-676= 224 degrees. That is the missing interior angle.

Answer:

2. ⅕

Step-by-step explanation:

⅖ = European (½) = 2/10 = ⅕

Answer:

N = 5

Step-by-step explanation:

6 (2n - 8) = 12

12n - 48 = 12

12n = 60

n = 5

HOPE THIS HELPS

PLZZ MARK BRAINLEIST

Answer:

5 = n (i think)

Step-by-step explanation:

6(2(5)- 8) = 12

6(10 - 8)= 12

6 (2) = 12

Answer:

-12

Step-by-step explanation:

To evaluate the expression the known value of a = -8 can be substituted in so the equation becomes -8 - 4.

From there the subtraction can be completed which equals -12. This can be visually seen on a number line if you look at -8 and move left 4 spaces.

Answer:

The correct answer is:

P(nuts)=7/9

Step-by-step explanation:

The experimental probability that the next sundae sold will have nuts is

7/9

Experimental probability calculates the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event

\(P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}\)

where, \(P_e(E)\)  is denoting the experimental probability of occurrence of E.

We are given that At Frosty Freeze, 14 of the last 18 sundaes sold had nuts.

Therefore,

Probability that the next sundae has nuts is 14/18 = 7/9.

Thus, Probability that the next sundae does not have nuts = 2/9

P(nuts)=7/9

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The values under and inside the radical is 4 and 129 respectively

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers. One supposes generally that a ≠ 0; those equations with a = 0 are considered degenerate because the equation then becomes linear or even simpler.

A quadratic equation is given as ax²+ bx+ c=0

this can be solved using formula x=( -b±√b²-4ac)/2a.

in the equation 2x²-10=7x, it can be Rearranged As 2x²-7x-10= 0

a= 2, b= -7 and c= -10

x= -(-7)±√(-7)²-4×2×-10)/2×2

x= 7±√49+80)/4

x= 7/4 ± √129/4

therefore the values inside and under the radical is 129 and 4

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y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job

x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).

y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.

y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.

y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.

y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.

Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

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The measure of angle ∠4 and angle ∠8 will be equal because they are corresponding angles. Then the correct option is D.

If two lines are parallel and the third line is transverse to it. Then the corresponding angles are equal to each other.

According to the equivalent angles postulate, if two parallel lines are intersected by a transverse, the corresponding inclination is identical.

From the diagram, the corresponding angles are given as,

∠1 = ∠5

∠2 = ∠6

∠3 = ∠7

∠4 = ∠8

The measure of angle ∠4 and angle ∠8 will be equal because they are corresponding angles. Then the correct option is D.

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The complete question is given below.

Which must be true by the corresponding angles

theorem?

a. ∠2 = ∠5

b. ∠1 = ∠6

c. ∠4 = ∠7

d. ∠4 = ∠8

The required solutions of the functions are given as follows,

1. f(−7) = 35

2. f(−1) =  -1

3. f(0) =  1

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
1 .
for x = -7
f(x) = x² + 2x
f(-7) = (-7)² + 2(-7) = 35

2.
for x = -1
f(x) = x² + 2x
f(−1) = (-1)² + 2(-1) = -1

3.
For x = 0
f(x) = x + 1

f(0) = 0 + 1 =  1

Thus, the required solutions are given as follows,

1. f(−7) = 35

2. f(−1) =  -1

3. f(0) =  1

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