A square root function has a domain of x≥2 and a range of y≥8.

What is the domain of its inverse?

Responses

x≥2
x is greater than or equal to 2

y≥8
y is greater than or equal to 8

x≥8
x is greater than or equal to 8

y≥2

Answer:

5n + 12p + 12m

Step-by-step explanation:

Perimeter means you are adding up all three sides.

4m + 3n + 8m + 10p + 2p + 2n

= 2n+3n + 10p+2p + 4m+8m

Combine like terms.

= 5n + 12p + 12m

The answer is,

Yes, the residual plot lacks a recognizable pattern.

So, the correct option is c

A simple random sample, in which each participant has an equal chance of being chosen, chooses a small, random portion of the whole population to represent the entire data set.

Researchers may produce an uncomplicated random sample by using methods like lotteries or random draws.

A sampling error may have occurred if the sample does not accurately reflect the population it is supposed to represent.

By selecting values at random from a population and giving each item a series of values, simple random samples are produced.

Simple random sampling is a sample design option to systematic, stratified, or cluster sampling.

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The double angle results are;

sin 2x = 62/64

cos 2x = 14/64

tan 2x = 384/83

We can see that it is possible for an angle to be given in the double angle format and we need to obtain the angles from it.

We know that sin x = 5/8

Using the Pythagoras theorem;

c^2 = a^2 + b^2

c = 8

a= 5

b= √c^2 - a^2

b = √ 8^2 - 5^2

b = √ 64 -25

b= 6.2

cos x = 6.2/8

Tan x = 5/6.2

Then;

sin2x = 2 sinxcosx

sin 2x = 2(5/8 × 6.2/8)

sin2x = 2(31/64)

sin2x = 62/64

cos 2x = 1 - 2sin^2x

cos 2x = 1 - 2(5/8)^2

cos 2x = 1 - 2(25/64)

cos 2x = 1 - 50/64

cos 2x = 14/64

Tan 2x = 2tan x/1 - tan^2 x

tan 2x = 2 (5/6.2)/1 - (5/6.2)^2

tan 2x = 10/6.2/1 - 25/38.4

tan2x = 10/6.2/13.4/38.4

tan2x = 10/6.2 * 38.4/13.4

tan 2x = 384/83

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The simplification form of expression 4(3x + 2) −2 is 12x + 6, and the factor of the expression 20b − 16 is 4 (5b - 4).

The expression is given in the question

4(3x + 2) −2

Apply the distributive property of multiplication,

4×3x + 4 × 2 −2

12x + 8 - 2

Apply subtraction operation,

12x + 6

The expression is given in the question

20b − 16

To determine the factor of the expression

20b − 16

5 × 4 × b - 4 × 4

Factor out 4 in the above expression

4 (5b - 4)

Thus, the simplification form of expression 4(3x + 2) −2 is 12x + 6, and the factor of the expression 20b − 16 is 4 (5b - 4).

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The equation 36-7p=-7p-35 has no solution.

What is equation?

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the expression on the right from the expressions on both sides, this won't reduce the generality.

Here the given equation is

=> 36-7p=-7p-35

=>-7p+7p=-35-36

=>0=71

Then the statement is false for any value of p.

Hence the given equation has no solution.

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For the given equation, c = 11.5t where t is the number of tickets to watch movie and c is the total cost to watch movie then table representing the equation is given by

option B:

Number of tickets :     1             2

Cost in dollars      :    $11.50      $23

As given in the question,

Given equation to represents the total cost to watch a movie related to number of tickets of movie.

c = 11.5t

Where t is the number of tickets to watch movie and c is the total cost to watch movie.

Table which represents the given situation is given by:

Option A:

Number of tickets cannot be in decimals that is 0.09 and 0.17.

Incorrect.

Option B.

Number of ticket  = 1

cost 'c' = 11.5(1)

          = $11.5

when t = 2

c = 11.5(2)

  = $23

Correct.

Option C:

Number of tickets cannot be in decimals that is 11.5.

Option D:

when t = 1

c = $0.09 is incorrect.

Therefore, For the given equation, c = 11.5t where t is the number of tickets to watch movie and c is the total cost to watch movie then table representing the equation is given by

option B:

Number of tickets :     1               2

Cost in dollars      :    $11.50      $23

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The correct option is C.

The statement best describes the solution set to the inequality as the solution set includes all values of x greater than -8 and less than 9.

Inequality: An inequality is an expression that shows an unequal comparison of two or more numbers and variables.

Given that:

Inequality

0 < 8 + x < 17

Adding on both sides by -8.

=> 0 - 8 < 8 + x - 8 < 17 - 8

=> -8 < x < 9

The solution set is (-8,9).

Therefore, the solution set includes the value of x greater than -8 and less than 9.

Hence, the correct statement that best describes the solution is option C.

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Answer:

64 marbles

Step-by-step explanation:

hope it helped :)

There are numerous reasons to use number lines to teach positive and negative numbers. But the following which is not used number line is B) Number lines match several familiar situations, like altitude, temperature, and football.

What is number line?

   A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, the whole number is a collection of numbers that contains both zero (0) and all counting numbers (1, 2, 3,4,5,6), whereas the natural number is a collection of all counting numbers (1, 2, 3,4, 5, 6). Comparing numbers is made simpler by writing them on a number line. As seen in the aforementioned graphic, the integers on the left are smaller than the integers on the right. For instance, 0 is lower than 1 and -1

Here the reasons we use number line for to teach positive and negative numbers is ,

=> Children are taught the fundamentals of addition and subtraction in mathematics using number lines with negative and positive numbers. It can also be used to multiply by skipping counts. The use of positive or negative signs makes it challenging to solve equations involving negative integers on a number line.

=> Number lines can be utilised in a variety of various ways, despite the fact that it may seem like addition, subtraction, and multiplication principles are best taught to children using number lines. The negative number line and positive number line are used by people to compute and measure specifics. These lines display the values' substantial increases and decreases.

Therefore the correct option is B)Number lines match several familiar situations, like altitude, temperature, and football.

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A. The equation that represents the situation is $9.98 = c + $2.47

B. The solution using a related equation $.7.51

C. The solution of the equation represents the initial cost of the toy before the increment of price.

Equation:

Basically, the equation means the mathematical statement that is made up of two expressions connected by an equal sign.

Given,

Because it is popular, a store owner increases the cost of a toy by $2.47. The new cost of the toy is $9.98.

Here we need to find the following:

A. The equation that represents the situation

B. The solution using a related equation

C. The solution of the equation represent.

Here we know that the new cost of the toy is equal to the original cost of the toy plus the amount by which cost was increased.

So, the equation is written as,

=> New cost of the toy = original cost + amount of increase

=> $9.98 = c + $2.47

Here we need to determine the value of c, make c the subject of the formula by combining similar terms

So, the equation is rewritten as,

=> c = $9.98 - $2.47

=> c = $7.51

Therefore, the initial cost of the toy is $.7,51

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Answer: x=16

Step-by-step explanation:

log₇(3x²+x)-log₇x=2

Domian:

1)

3x²+x>0

x(3x+1)>0

-∞__+__-1/3__-__0__+__∞

x∈(-∞,-1/3)U(0,∞)

2)

x>0

Hence, x∈(0,∞)

Thus x∈(0,∞)

In this problem we use the following formula:

                       [tex]\boxed {log_ax-log_ay=log_a\frac{x}{y}}[/tex]

[tex]\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\Hence,\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\ Divide\ both\ parts \ of\ the \ equation\ by\ 3:\\\\x=16[/tex]

The extraneous solution to the logarithmic equation log7 (3x³ + x)-log7(x)=2 is x= 4.

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.

We have Logarithmic expression as

log7 (3x³ + x)-log7(x)=2

we know, [tex]log_ax - log_a y= log_a (x/y)[/tex]

Using the above property as

log7 (3x³ + x)-log7(x)=2

[tex]log_7[/tex] (3x³ + x) - [tex]log_7[/tex] x =2

[tex]log_7[/tex] x(3x² +1) / x = 2

[tex]log_7[/tex] (3x²+1) = 2(1)

[tex]log_7[/tex] (3x²+1) = 2(1)[tex]log_7 (7)[/tex]

[tex]log_7[/tex] (3x²+1) = [tex]log_7[/tex]7²

Now, comparing we get

3x² +1 = 7²

3x² = 48

x² = 16

x = 4

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Answer:

the answer is 100...........

The amount of calling for which the two plans cost the same will be 525 minutes.

The cost when two plans cost the same amount is $68.25.

The minimum number of nickels that Jaxson could have is 9.

Given that, Jaxson has some pennies and some nickels.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let the number of pennies be P and the number of nickels be N.

So, P + N > 13

Therefore

P×0.01 + N×0.05 ≥ 0.33

Because he has at most, $0.33

If  P = 4

4×0.01 + N0.05 ≥ 0.33

∵ $0.33 - $0.04 = $0.29

N×0.05≥ 0.29

N = 0.29/0.05 = 5.8

The number of nickels that he might have is 9.6, but because he cannot have 0.6 of a nickel, we have to round the figure down to 9.

Now that we also know that he had at least 15 coins in total, we can use that equation to get the smallest possible number for N.

4 +  N  > 13

N > 13 - 4

N> 9

So we have the range:

9 < N ≤ 5.8

Therefore, the minimum number of nickels that Jaxson could have is 9.

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Answer:

y = 4/3 x + 4/3

Step-by-step explanation:

y - (-4) = 4/3(x-(-4)

y+4 = 4/3 (x +4)

y + 4 = 4/3 x + 16/3

y = 4/3 x +16/3 -4

y = 4/3 x + (16- 12)/3

y = 4/3 x + 4/3

y = 4/3 x + 4/3

Answer:

y=4/3x+4/3

Step-by-step explanation:

-4=4/3(-4)+9

-4=-16/3+9

-4=-5 1/3+9

-4= 4 1/3

4+4 1/3=8 1/3

9-8 1/3=2/3

-4=4/3(-4)+2/3

-4=-16/3+2/3

-4=-14/3

-4=-4 2/3

2/3+2/3=4/3

-4=4/3(-4)+4/3

-4=-16/3+4/3

-4=-12/3

-4=-4

The equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".

Two or more expressions with an equal sign are defined as an equation.

The given equation is Three-fifths(30x -  15) = 72.

Simplify the equation as follows:
Three-fifths(30x -  15) = 72

3/5(30x - 15) = 72

18x - 9 = 72

Which is equivalent to "18x minus 9 = 72".

Solve for the  value of x:

18x -9 = 72

18x = 72 + 9

18x = 81

x = 81/18

x = 27/6

x = 4.5

Now, solve the equation in the first option:

18x - 15 = 72

18x = 87

x = 4.83

Solve the equation in the second option:

50x - 25 = 72

50x = 97

x = 1.94

The third equation is already shown to be equivalent to the given equation.

The solution to the fourth equation is:

3(6x - 3) = 72

18x -9 =72

Which is the same as the given equation.

The last equation is x = 4.5

Hence, the equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".

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In coordinate system, the number that is the abscissa of the point ( 8,7 ) is 8.

coordinate geometry:

It establishes a connection between geometry and algebra using curves and line graphs.

A point's x and y coordinates are also referred to as abscissa and ordinate, respectively.

the abscissa is the x–coordinate of any point A(x, y).

so,

abscissa of the point ( 8,7 ) is 8.

In coordinate system, the number that is the abscissa of the point ( 8,7 ) is 8.

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Answer:

x = 78

Step-by-step explanation:

[tex]\frac{8}{24} =\frac{26}{x}[/tex]

==> cross multiply

26 x 24 = 8 x "x"

==> simplify

624 = 8x

==> divide both sides by 8

78 = x

Answer: x = 78

Step-by-step explanation:

It is 78 because if you cross-multiply, you get 624 = 8x. Then if you divide by 8 on both sides, you get x = 78.

The function F(x) = -3x² + 18x + 3 has a maximum value of 30 at x = 3

From the question, we have the following equation that can be used in our computation:

F(x) = -3x² + 18x + 3

A quadratic function is represented as

F(x) = ax² + bx + 3

By comparison, we have

a = -3

For a quadratic function to have a maximum value, the value of a must be less than 0

This means that the function has a maximum value because -3 is less than 0

Solving further, we have

F(x) = -3x² + 18x + 3

Differentiate and set to 0

-6x + 18 = 0

So, we have

x = 3

Substitute x = 3 in F(x)

F(3) = -3(3)² + 18(3) + 3

Evaluate

F(3) = 30

This represents the maximum value

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The number of hours at which both companies' rental costs will be the same is nearly 6 hours.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions displayed on the left and right sides have an equal connection. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved.

Let the number of hours = h The deposit price at the first canoe rental company = $10

Cost per hour to rent a canoe = $8.25/h

The total cost for rental for the first company is given by

C(A) = 10 + 8.25h

The deposit price at the second canoe rental company = $12.50

Cost per hour to rent a canoe = $7.85/h

The total cost for rental for the second company is given by

C(B) = 12.50 + 7.85h

The number of hours at which both company's rental costs will be the same is given as

C(A) = C(B)

10 + 8.25h = 12.50 + 7.85h

8.25h - 7.85h = 12.50 - 10

0.4h = 2.5

h = 2.5/0.4

h = 6.25

h ≈ 6 hours

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The most important to determine before allowing employees to access the server remotely is B. security method of allowing connections.

What is a computer network?

Computer networking refers to the interconnection of computing devices that can exchange data and share resources. These networked devices use a set of rules known as communications protocols to transmit data over physical or wireless networks.

A computer network is a collection of computers that share resources that are located on or provided by network nodes. To communicate with one another, the computers use common communication protocols over digital interconnections.

Local-area networks (LANs) and wide-area networks (WANs) are the two basic network types (WANs). LANs connect computers and peripheral devices in a constrained physical area, such as a business office, laboratory, or college campus, using data-transmitting links (wires, Ethernet cables, fiber optics, Wi-Fi).

In this case, it should be noted that the security method that's used for allowing the connection is important. Based on the information illustrated, the correct option is B.

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Answer:

it can be 100 because percentages are out of 100

The number of terms in the arithmetic sequence {-8, 1, 10, 19, 28, ..., 469} is 54 terms

The number of terms in the sequence { -8, 1, 10, 19, 28, ..., 469 } is calculated from the formula

Un = a1 + (n - 1) d

where a1 = first term

d = common difference

n = number of terms

a = -8

d = second term -  first term

= 1 - -8

= 9

solving for n

Un = a1 + (n - 1) d

469 = -8 + (n - 1)9

469 + 8 = (n - 1)9

collecting like terms

(n - 1) = 477 / 9

n - 1 = 53

n = 54

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By using natural logarithm properties we will see that the solutions of the two equations are:

17) x = 3.11

19) p = 2.02

Here we will use the property of natural logarithms:

Ln( a^x) = x*ln(a)

17) We have the exponential equation:

5^(x - 2) = 6

If we apply the natural logarithm in both sides, we will get:

ln( 5^(x - 2)) = ln(6)

(x - 2)*ln(5) = ln(6)

(x - 2) = ln(6)/ln(5)

x = ln(6)/ln(5) + 2

x = 3.11

19) Now the exponential equation is:

7^p = 51

We will do the exact same thing, apply the natural logarithm in both sides:

ln(7^p) = ln(51)

p*ln(7) = ln(51)

p = ln(51)/ln(7) = 2.02

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Answer:

[tex] \huge{ \bold{y = - 2x - 5}}[/tex]

Step-by-step explanation:

The equation of a line in slope-intercept form is represented by

y = mx + c

where

m is the slope

c is the y-intercept

First of all we have to find the slope from the two points given by using the formula

[tex]m = \frac{y_2 -y_ 1}{x_2 -x_1 } \\ [/tex]

where

(x1, y1) and (x2, y2) are the points

From the question the points are (-3,1) and (4, -13)

We have

[tex]m = \frac{ - 13 - 1}{4 - - 3} = \frac{ - 13 - 1}{4 + 3} = - \frac{14}{7} = - 2 \\ [/tex]

Next we find the y-intercept 'c' by placing one of the points and the slope into the slope-intercept form equation

Using point (-3,1) and m = -2

We have

[tex]1 = ( - 2)( - 3) + c \\ 1 = 6 +c \\ c = 1 - 6 = - 5[/tex]

Since we have both m and c we can place it into the main equation to find the equation

Using point and m = -2 c= -5

We have the final answer as

[tex] \bold{y = - 2x - 5}[/tex]

Hope this helps you

The shape of units you would get that has a perimeter of 22 and an area of 30 is a rectangle, which is shown in the image below.

A rectangle is a quadrilateral that has two opposite sides that are equal and are longer than the other two opposite sides that are equal and parallel to each other.

Assuming that the shape being referred to is a rectangle that has an area of 30 units² and a perimeter of 22 units, therefore, the dimensions of the rectangle is shown in the image attached below, and they are:

Length of rectangle = 6 units

Width of rectangle = 5 units

Therefore:

Area of the rectangle = 6 × 5 = 30 units².

Perimeter of the rectangle = 2(6 + 5) = 2(11) = 22 units.

This implies that the shape of units with an area of 30 units² and a perimeter of 22 units is most likely a rectangle.

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Answer:

C

Step-by-step explanation:

to find the unit rate divide miles travelled by petrol used , that is

60 [tex]\frac{2}{3}[/tex] ÷ 4 [tex]\frac{2}{3}[/tex] ← change mixed numbers to improper fractions

= [tex]\frac{182}{3}[/tex] ÷ [tex]\frac{14}{3}[/tex]

• leave first fraction, change ÷ to × , turn second fraction ' upside down'

= [tex]\frac{182}{3}[/tex] × [tex]\frac{3}{14}[/tex] ( cancel 3 on numerator/ denominator )

= 182 × [tex]\frac{1}{14}[/tex]

= [tex]\frac{182}{14}[/tex]

= 13

the car travels 13 miles per gallon of petrol

y=−1/2x+1/2

Step-by-step explanation: